A-PRIORI-Algorithm

This is the Problems 6.2.6(a) from the “Mining Massive Data set” text book (Page 199) programmatic solution

Apply the A-Priori Algorithm with support threshold 5 to the data of: Exercise 6.1.1 : Suppose there are 100 items, numbered 1 to 100, and also 100 baskets, also numbered 1 to 100. Item i is in basket b if and only if i divides b with no remainder. Thus, item 1 is in all the baskets, item 2 is in all fifty of the even-numbered baskets, and so on. Basket 12 consists of items {1, 2, 3, 4, 6, 12}, since these are all the integers that divide 12.

The Code Output: Freqent items with support threshold 5 are : L1= 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 count = 20

Generating 2-itemset Freqent pattern with support threshold 5:

C2= 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 1 11 1 12 1 13 1 14 1 15 1 16 1 17 1 18 1 19 1 20 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 3 20 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 6 7 6 8 6 9 6 10 6 11 6 12 6 13 6 14 6 15 6 16 6 17 6 18 6 19 6 20 7 8 7 9 7 10 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 8 9 8 10 8 11 8 12 8 13 8 14 8 15 8 16 8 17 8 18 8 19 8 20 9 10 9 11 9 12 9 13 9 14 9 15 9 16 9 17 9 18 9 19 9 20 10 11 10 12 10 13 10 14 10 15 10 16 10 17 10 18 10 19 10 20 11 12 11 13 11 14 11 15 11 16 11 17 11 18 11 19 11 20 12 13 12 14 12 15 12 16 12 17 12 18 12 19 12 20 13 14 13 15 13 16 13 17 13 18 13 19 13 20 14 15 14 16 14 17 14 18 14 19 14 20 15 16 15 17 15 18 15 19 15 20 16 17 16 18 16 19 16 20 17 18 17 19 17 20 18 19 18 20 19 20

L2= 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 1 11 1 12 1 13 1 14 1 15 1 16 1 17 1 18 1 19 1 20 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 12 2 14 2 16 2 18 2 20 3 4 3 5 3 6 3 9 3 12 3 15 3 18 4 5 4 6 4 8 4 10 4 12 4 16 4 20 5 10 5 15 5 20 6 9 6 12 6 18 7 14 8 16 9 18 10 20 count = 56

Generating 3-itemset Freqent pattern with support threshold 5:

C3= 1 2 3 1 2 4 1 2 5 1 2 6 1 2 7 1 2 8 1 2 9 1 2 10 1 2 12 1 2 14 1 2 16 1 2 18 1 2 20 1 3 4 1 3 5 1 3 6 1 3 9 1 3 12 1 3 15 1 3 18 1 4 5 1 4 6 1 4 8 1 4 10 1 4 12 1 4 16 1 4 20 1 5 10 1 5 15 1 5 20 1 6 9 1 6 12 1 6 18 1 7 14 1 8 16 1 9 18 1 10 20 2 3 4 2 3 5 2 3 6 2 3 9 2 3 12 2 3 18 2 4 5 2 4 6 2 4 8 2 4 10 2 4 12 2 4 16 2 4 20 2 5 10 2 5 20 2 6 9 2 6 12 2 6 18 2 7 14 2 8 16 2 9 18 2 10 20 3 4 5 3 4 6 3 4 12 3 5 15 3 6 9 3 6 12 3 6 18 3 9 18 4 5 10 4 5 20 4 6 12 4 8 16 4 10 20 5 10 20 6 9 18

L3= 1 2 3 1 2 4 1 2 5 1 2 6 1 2 7 1 2 8 1 2 9 1 2 10 1 2 12 1 2 14 1 2 16 1 2 18 1 2 20 1 3 4 1 3 5 1 3 6 1 3 9 1 3 12 1 3 15 1 3 18 1 4 5 1 4 6 1 4 8 1 4 10 1 4 12 1 4 16 1 4 20 1 5 10 1 5 15 1 5 20 1 6 9 1 6 12 1 6 18 1 7 14 1 8 16 1 9 18 1 10 20 2 3 4 2 3 6 2 3 9 2 3 12 2 3 18 2 4 5 2 4 6 2 4 8 2 4 10 2 4 12 2 4 16 2 4 20 2 5 10 2 5 20 2 6 9 2 6 12 2 6 18 2 7 14 2 8 16 2 9 18 2 10 20 3 4 6 3 4 12 3 5 15 3 6 9 3 6 12 3 6 18 3 9 18 4 5 10 4 5 20 4 6 12 4 8 16 4 10 20 5 10 20 6 9 18 count = 72

Generating 4-itemset Freqent pattern with support threshold 5:

C4= 1 2 3 4 1 2 3 6 1 2 3 9 1 2 3 12 1 2 3 18 1 2 4 5 1 2 4 6 1 2 4 8 1 2 4 10 1 2 4 12 1 2 4 16 1 2 4 20 1 2 5 10 1 2 5 20 1 2 6 9 1 2 6 12 1 2 6 18 1 2 7 14 1 2 8 16 1 2 9 18 1 2 10 20 1 3 4 6 1 3 4 12 1 3 5 15 1 3 6 9 1 3 6 12 1 3 6 18 1 3 9 18 1 4 5 10 1 4 5 20 1 4 6 12 1 4 8 16 1 4 10 20 1 5 10 20 1 6 9 18 2 3 4 6 2 3 4 12 2 3 6 9 2 3 6 12 2 3 6 18 2 3 9 18 2 4 5 10 2 4 5 20 2 4 6 12 2 4 8 16 2 4 10 20 2 5 10 20 2 6 9 18 3 4 6 12 3 6 9 18 4 5 10 20

L4= 1 2 3 4 1 2 3 6 1 2 3 9 1 2 3 12 1 2 3 18 1 2 4 5 1 2 4 6 1 2 4 8 1 2 4 10 1 2 4 12 1 2 4 16 1 2 4 20 1 2 5 10 1 2 5 20 1 2 6 9 1 2 6 12 1 2 6 18 1 2 7 14 1 2 8 16 1 2 9 18 1 2 10 20 1 3 4 6 1 3 4 12 1 3 5 15 1 3 6 9 1 3 6 12 1 3 6 18 1 3 9 18 1 4 5 10 1 4 5 20 1 4 6 12 1 4 8 16 1 4 10 20 1 5 10 20 1 6 9 18 2 3 4 6 2 3 4 12 2 3 6 9 2 3 6 12 2 3 6 18 2 3 9 18 2 4 5 10 2 4 5 20 2 4 6 12 2 4 8 16 2 4 10 20 2 5 10 20 2 6 9 18 3 4 6 12 3 6 9 18 4 5 10 20 count = 51

Generating 5-itemset Freqent pattern with support threshold 5:

C5= 1 2 3 4 6 1 2 3 4 12 1 2 3 6 9 1 2 3 6 12 1 2 3 6 18 1 2 3 9 18 1 2 4 5 10 1 2 4 5 20 1 2 4 6 12 1 2 4 8 16 1 2 4 10 20 1 2 5 10 20 1 2 6 9 18 1 3 4 6 12 1 3 6 9 18 1 4 5 10 20 2 3 4 6 12 2 3 6 9 18 2 4 5 10 20

L5= 1 2 3 4 6 1 2 3 4 12 1 2 3 6 9 1 2 3 6 12 1 2 3 6 18 1 2 3 9 18 1 2 4 5 10 1 2 4 5 20 1 2 4 6 12 1 2 4 8 16 1 2 4 10 20 1 2 5 10 20 1 2 6 9 18 1 3 4 6 12 1 3 6 9 18 1 4 5 10 20 2 3 4 6 12 2 3 6 9 18 2 4 5 10 20 count = 19

Generating 6-itemset Freqent pattern with support threshold 5:

C6= 1 2 3 4 6 12 1 2 3 6 9 18 1 2 4 5 10 20

L6= 1 2 3 4 6 12 1 2 3 6 9 18 1 2 4 5 10 20 count = 3

Generating 7-itemset Freqent pattern with support threshold 5:

C7=

Given the minimum confidence threthold of 90%, the resulting association rules are:

Lets take L = {1 2 } Selected Rules are: R1: { 2 } -> { 1 } confidence = 50/50 = 100.00%

Lets take L = {1 3 } Selected Rules are: R2: { 3 } -> { 1 } confidence = 33/33 = 100.00%

Lets take L = {1 4 } Selected Rules are: R3: { 4 } -> { 1 } confidence = 25/25 = 100.00%

Lets take L = {1 5 } Selected Rules are: R4: { 5 } -> { 1 } confidence = 20/20 = 100.00%

Lets take L = {1 6 } Selected Rules are: R5: { 6 } -> { 1 } confidence = 16/16 = 100.00%

Lets take L = {1 7 } Selected Rules are: R6: { 7 } -> { 1 } confidence = 14/14 = 100.00%

Lets take L = {1 8 } Selected Rules are: R7: { 8 } -> { 1 } confidence = 12/12 = 100.00%

Lets take L = {1 9 } Selected Rules are: R8: { 9 } -> { 1 } confidence = 11/11 = 100.00%

Lets take L = {1 10 } Selected Rules are: R9: { 10 } -> { 1 } confidence = 10/10 = 100.00%

Lets take L = {1 11 } Selected Rules are: R10: { 11 } -> { 1 } confidence = 9/9 = 100.00%

Lets take L = {1 12 } Selected Rules are: R11: { 12 } -> { 1 } confidence = 8/8 = 100.00%

Lets take L = {1 13 } Selected Rules are: R12: { 13 } -> { 1 } confidence = 7/7 = 100.00%

Lets take L = {1 14 } Selected Rules are: R13: { 14 } -> { 1 } confidence = 7/7 = 100.00%

Lets take L = {1 15 } Selected Rules are: R14: { 15 } -> { 1 } confidence = 6/6 = 100.00%

Lets take L = {1 16 } Selected Rules are: R15: { 16 } -> { 1 } confidence = 6/6 = 100.00%

Lets take L = {1 17 } Selected Rules are: R16: { 17 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 18 } Selected Rules are: R17: { 18 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 19 } Selected Rules are: R18: { 19 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 20 } Selected Rules are: R19: { 20 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {2 3 } Selected Rules are:

Lets take L = {2 4 } Selected Rules are: R20: { 4 } -> { 2 } confidence = 25/25 = 100.00%

Lets take L = {2 5 } Selected Rules are:

Lets take L = {2 6 } Selected Rules are: R21: { 6 } -> { 2 } confidence = 16/16 = 100.00%

Lets take L = {2 7 } Selected Rules are:

Lets take L = {2 8 } Selected Rules are: R22: { 8 } -> { 2 } confidence = 12/12 = 100.00%

Lets take L = {2 9 } Selected Rules are:

Lets take L = {2 10 } Selected Rules are: R23: { 10 } -> { 2 } confidence = 10/10 = 100.00%

Lets take L = {2 12 } Selected Rules are: R24: { 12 } -> { 2 } confidence = 8/8 = 100.00%

Lets take L = {2 14 } Selected Rules are: R25: { 14 } -> { 2 } confidence = 7/7 = 100.00%

Lets take L = {2 16 } Selected Rules are: R26: { 16 } -> { 2 } confidence = 6/6 = 100.00%

Lets take L = {2 18 } Selected Rules are: R27: { 18 } -> { 2 } confidence = 5/5 = 100.00%

Lets take L = {2 20 } Selected Rules are: R28: { 20 } -> { 2 } confidence = 5/5 = 100.00%

Lets take L = {3 4 } Selected Rules are:

Lets take L = {3 5 } Selected Rules are:

Lets take L = {3 6 } Selected Rules are: R29: { 6 } -> { 3 } confidence = 16/16 = 100.00%

Lets take L = {3 9 } Selected Rules are: R30: { 9 } -> { 3 } confidence = 11/11 = 100.00%

Lets take L = {3 12 } Selected Rules are: R31: { 12 } -> { 3 } confidence = 8/8 = 100.00%

Lets take L = {3 15 } Selected Rules are: R32: { 15 } -> { 3 } confidence = 6/6 = 100.00%

Lets take L = {3 18 } Selected Rules are: R33: { 18 } -> { 3 } confidence = 5/5 = 100.00%

Lets take L = {4 5 } Selected Rules are:

Lets take L = {4 6 } Selected Rules are:

Lets take L = {4 8 } Selected Rules are: R34: { 8 } -> { 4 } confidence = 12/12 = 100.00%

Lets take L = {4 10 } Selected Rules are:

Lets take L = {4 12 } Selected Rules are: R35: { 12 } -> { 4 } confidence = 8/8 = 100.00%

Lets take L = {4 16 } Selected Rules are: R36: { 16 } -> { 4 } confidence = 6/6 = 100.00%

Lets take L = {4 20 } Selected Rules are: R37: { 20 } -> { 4 } confidence = 5/5 = 100.00%

Lets take L = {5 10 } Selected Rules are: R38: { 10 } -> { 5 } confidence = 10/10 = 100.00%

Lets take L = {5 15 } Selected Rules are: R39: { 15 } -> { 5 } confidence = 6/6 = 100.00%

Lets take L = {5 20 } Selected Rules are: R40: { 20 } -> { 5 } confidence = 5/5 = 100.00%

Lets take L = {6 9 } Selected Rules are:

Lets take L = {6 12 } Selected Rules are: R41: { 12 } -> { 6 } confidence = 8/8 = 100.00%

Lets take L = {6 18 } Selected Rules are: R42: { 18 } -> { 6 } confidence = 5/5 = 100.00%

Lets take L = {7 14 } Selected Rules are: R43: { 14 } -> { 7 } confidence = 7/7 = 100.00%

Lets take L = {8 16 } Selected Rules are: R44: { 16 } -> { 8 } confidence = 6/6 = 100.00%

Lets take L = {9 18 } Selected Rules are: R45: { 18 } -> { 9 } confidence = 5/5 = 100.00%

Lets take L = {10 20 } Selected Rules are: R46: { 20 } -> { 10 } confidence = 5/5 = 100.00%

Lets take L = {1 2 3 } Selected Rules are: R47: { 2 3 } -> { 1 } confidence = 16/16 = 100.00%

Lets take L = {1 2 4 } Selected Rules are: R48: { 4 } -> { 1 2 } confidence = 25/25 = 100.00% R49: { 1 4 } -> { 2 } confidence = 25/25 = 100.00% R50: { 2 4 } -> { 1 } confidence = 25/25 = 100.00%

Lets take L = {1 2 5 } Selected Rules are: R51: { 2 5 } -> { 1 } confidence = 10/10 = 100.00%

Lets take L = {1 2 6 } Selected Rules are: R52: { 6 } -> { 1 2 } confidence = 16/16 = 100.00% R53: { 1 6 } -> { 2 } confidence = 16/16 = 100.00% R54: { 2 6 } -> { 1 } confidence = 16/16 = 100.00%

Lets take L = {1 2 7 } Selected Rules are: R55: { 2 7 } -> { 1 } confidence = 7/7 = 100.00%

Lets take L = {1 2 8 } Selected Rules are: R56: { 8 } -> { 1 2 } confidence = 12/12 = 100.00% R57: { 1 8 } -> { 2 } confidence = 12/12 = 100.00% R58: { 2 8 } -> { 1 } confidence = 12/12 = 100.00%

Lets take L = {1 2 9 } Selected Rules are: R59: { 2 9 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 2 10 } Selected Rules are: R60: { 10 } -> { 1 2 } confidence = 10/10 = 100.00% R61: { 1 10 } -> { 2 } confidence = 10/10 = 100.00% R62: { 2 10 } -> { 1 } confidence = 10/10 = 100.00%

Lets take L = {1 2 12 } Selected Rules are: R63: { 12 } -> { 1 2 } confidence = 8/8 = 100.00% R64: { 1 12 } -> { 2 } confidence = 8/8 = 100.00% R65: { 2 12 } -> { 1 } confidence = 8/8 = 100.00%

Lets take L = {1 2 14 } Selected Rules are: R66: { 14 } -> { 1 2 } confidence = 7/7 = 100.00% R67: { 1 14 } -> { 2 } confidence = 7/7 = 100.00% R68: { 2 14 } -> { 1 } confidence = 7/7 = 100.00%

Lets take L = {1 2 16 } Selected Rules are: R69: { 16 } -> { 1 2 } confidence = 6/6 = 100.00% R70: { 1 16 } -> { 2 } confidence = 6/6 = 100.00% R71: { 2 16 } -> { 1 } confidence = 6/6 = 100.00%

Lets take L = {1 2 18 } Selected Rules are: R72: { 18 } -> { 1 2 } confidence = 5/5 = 100.00% R73: { 1 18 } -> { 2 } confidence = 5/5 = 100.00% R74: { 2 18 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 2 20 } Selected Rules are: R75: { 20 } -> { 1 2 } confidence = 5/5 = 100.00% R76: { 1 20 } -> { 2 } confidence = 5/5 = 100.00% R77: { 2 20 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 3 4 } Selected Rules are: R78: { 3 4 } -> { 1 } confidence = 8/8 = 100.00%

Lets take L = {1 3 5 } Selected Rules are: R79: { 3 5 } -> { 1 } confidence = 6/6 = 100.00%

Lets take L = {1 3 6 } Selected Rules are: R80: { 6 } -> { 1 3 } confidence = 16/16 = 100.00% R81: { 1 6 } -> { 3 } confidence = 16/16 = 100.00% R82: { 3 6 } -> { 1 } confidence = 16/16 = 100.00%

Lets take L = {1 3 9 } Selected Rules are: R83: { 9 } -> { 1 3 } confidence = 11/11 = 100.00% R84: { 1 9 } -> { 3 } confidence = 11/11 = 100.00% R85: { 3 9 } -> { 1 } confidence = 11/11 = 100.00%

Lets take L = {1 3 12 } Selected Rules are: R86: { 12 } -> { 1 3 } confidence = 8/8 = 100.00% R87: { 1 12 } -> { 3 } confidence = 8/8 = 100.00% R88: { 3 12 } -> { 1 } confidence = 8/8 = 100.00%

Lets take L = {1 3 15 } Selected Rules are: R89: { 15 } -> { 1 3 } confidence = 6/6 = 100.00% R90: { 1 15 } -> { 3 } confidence = 6/6 = 100.00% R91: { 3 15 } -> { 1 } confidence = 6/6 = 100.00%

Lets take L = {1 3 18 } Selected Rules are: R92: { 18 } -> { 1 3 } confidence = 5/5 = 100.00% R93: { 1 18 } -> { 3 } confidence = 5/5 = 100.00% R94: { 3 18 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 4 5 } Selected Rules are: R95: { 4 5 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 4 6 } Selected Rules are: R96: { 4 6 } -> { 1 } confidence = 8/8 = 100.00%

Lets take L = {1 4 8 } Selected Rules are: R97: { 8 } -> { 1 4 } confidence = 12/12 = 100.00% R98: { 1 8 } -> { 4 } confidence = 12/12 = 100.00% R99: { 4 8 } -> { 1 } confidence = 12/12 = 100.00%

Lets take L = {1 4 10 } Selected Rules are: R100: { 4 10 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 4 12 } Selected Rules are: R101: { 12 } -> { 1 4 } confidence = 8/8 = 100.00% R102: { 1 12 } -> { 4 } confidence = 8/8 = 100.00% R103: { 4 12 } -> { 1 } confidence = 8/8 = 100.00%

Lets take L = {1 4 16 } Selected Rules are: R104: { 16 } -> { 1 4 } confidence = 6/6 = 100.00% R105: { 1 16 } -> { 4 } confidence = 6/6 = 100.00% R106: { 4 16 } -> { 1 } confidence = 6/6 = 100.00%

Lets take L = {1 4 20 } Selected Rules are: R107: { 20 } -> { 1 4 } confidence = 5/5 = 100.00% R108: { 1 20 } -> { 4 } confidence = 5/5 = 100.00% R109: { 4 20 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 5 10 } Selected Rules are: R110: { 10 } -> { 1 5 } confidence = 10/10 = 100.00% R111: { 1 10 } -> { 5 } confidence = 10/10 = 100.00% R112: { 5 10 } -> { 1 } confidence = 10/10 = 100.00%

Lets take L = {1 5 15 } Selected Rules are: R113: { 15 } -> { 1 5 } confidence = 6/6 = 100.00% R114: { 1 15 } -> { 5 } confidence = 6/6 = 100.00% R115: { 5 15 } -> { 1 } confidence = 6/6 = 100.00%

Lets take L = {1 5 20 } Selected Rules are: R116: { 20 } -> { 1 5 } confidence = 5/5 = 100.00% R117: { 1 20 } -> { 5 } confidence = 5/5 = 100.00% R118: { 5 20 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 6 9 } Selected Rules are: R119: { 6 9 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 6 12 } Selected Rules are: R120: { 12 } -> { 1 6 } confidence = 8/8 = 100.00% R121: { 1 12 } -> { 6 } confidence = 8/8 = 100.00% R122: { 6 12 } -> { 1 } confidence = 8/8 = 100.00%

Lets take L = {1 6 18 } Selected Rules are: R123: { 18 } -> { 1 6 } confidence = 5/5 = 100.00% R124: { 1 18 } -> { 6 } confidence = 5/5 = 100.00% R125: { 6 18 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 7 14 } Selected Rules are: R126: { 14 } -> { 1 7 } confidence = 7/7 = 100.00% R127: { 1 14 } -> { 7 } confidence = 7/7 = 100.00% R128: { 7 14 } -> { 1 } confidence = 7/7 = 100.00%

Lets take L = {1 8 16 } Selected Rules are: R129: { 16 } -> { 1 8 } confidence = 6/6 = 100.00% R130: { 1 16 } -> { 8 } confidence = 6/6 = 100.00% R131: { 8 16 } -> { 1 } confidence = 6/6 = 100.00%

Lets take L = {1 9 18 } Selected Rules are: R132: { 18 } -> { 1 9 } confidence = 5/5 = 100.00% R133: { 1 18 } -> { 9 } confidence = 5/5 = 100.00% R134: { 9 18 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 10 20 } Selected Rules are: R135: { 20 } -> { 1 10 } confidence = 5/5 = 100.00% R136: { 1 20 } -> { 10 } confidence = 5/5 = 100.00% R137: { 10 20 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {2 3 4 } Selected Rules are: R138: { 3 4 } -> { 2 } confidence = 8/8 = 100.00%

Lets take L = {2 3 6 } Selected Rules are: R139: { 6 } -> { 2 3 } confidence = 16/16 = 100.00% R140: { 2 3 } -> { 6 } confidence = 16/16 = 100.00% R141: { 2 6 } -> { 3 } confidence = 16/16 = 100.00% R142: { 3 6 } -> { 2 } confidence = 16/16 = 100.00%

Lets take L = {2 3 9 } Selected Rules are: R143: { 2 9 } -> { 3 } confidence = 5/5 = 100.00%

Lets take L = {2 3 12 } Selected Rules are: R144: { 12 } -> { 2 3 } confidence = 8/8 = 100.00% R145: { 2 12 } -> { 3 } confidence = 8/8 = 100.00% R146: { 3 12 } -> { 2 } confidence = 8/8 = 100.00%

Lets take L = {2 3 18 } Selected Rules are: R147: { 18 } -> { 2 3 } confidence = 5/5 = 100.00% R148: { 2 18 } -> { 3 } confidence = 5/5 = 100.00% R149: { 3 18 } -> { 2 } confidence = 5/5 = 100.00%

Lets take L = {2 4 5 } Selected Rules are: R150: { 4 5 } -> { 2 } confidence = 5/5 = 100.00%

Lets take L = {2 4 6 } Selected Rules are: R151: { 4 6 } -> { 2 } confidence = 8/8 = 100.00%

Lets take L = {2 4 8 } Selected Rules are: R152: { 8 } -> { 2 4 } confidence = 12/12 = 100.00% R153: { 2 8 } -> { 4 } confidence = 12/12 = 100.00% R154: { 4 8 } -> { 2 } confidence = 12/12 = 100.00%

Lets take L = {2 4 10 } Selected Rules are: R155: { 4 10 } -> { 2 } confidence = 5/5 = 100.00%

Lets take L = {2 4 12 } Selected Rules are: R156: { 12 } -> { 2 4 } confidence = 8/8 = 100.00% R157: { 2 12 } -> { 4 } confidence = 8/8 = 100.00% R158: { 4 12 } -> { 2 } confidence = 8/8 = 100.00%

Lets take L = {2 4 16 } Selected Rules are: R159: { 16 } -> { 2 4 } confidence = 6/6 = 100.00% R160: { 2 16 } -> { 4 } confidence = 6/6 = 100.00% R161: { 4 16 } -> { 2 } confidence = 6/6 = 100.00%

Lets take L = {2 4 20 } Selected Rules are: R162: { 20 } -> { 2 4 } confidence = 5/5 = 100.00% R163: { 2 20 } -> { 4 } confidence = 5/5 = 100.00% R164: { 4 20 } -> { 2 } confidence = 5/5 = 100.00%

Lets take L = {2 5 10 } Selected Rules are: R165: { 10 } -> { 2 5 } confidence = 10/10 = 100.00% R166: { 2 5 } -> { 10 } confidence = 10/10 = 100.00% R167: { 2 10 } -> { 5 } confidence = 10/10 = 100.00% R168: { 5 10 } -> { 2 } confidence = 10/10 = 100.00%

Lets take L = {2 5 20 } Selected Rules are: R169: { 20 } -> { 2 5 } confidence = 5/5 = 100.00% R170: { 2 20 } -> { 5 } confidence = 5/5 = 100.00% R171: { 5 20 } -> { 2 } confidence = 5/5 = 100.00%

Lets take L = {2 6 9 } Selected Rules are: R172: { 2 9 } -> { 6 } confidence = 5/5 = 100.00% R173: { 6 9 } -> { 2 } confidence = 5/5 = 100.00%

Lets take L = {2 6 12 } Selected Rules are: R174: { 12 } -> { 2 6 } confidence = 8/8 = 100.00% R175: { 2 12 } -> { 6 } confidence = 8/8 = 100.00% R176: { 6 12 } -> { 2 } confidence = 8/8 = 100.00%

Lets take L = {2 6 18 } Selected Rules are: R177: { 18 } -> { 2 6 } confidence = 5/5 = 100.00% R178: { 2 18 } -> { 6 } confidence = 5/5 = 100.00% R179: { 6 18 } -> { 2 } confidence = 5/5 = 100.00%

Lets take L = {2 7 14 } Selected Rules are: R180: { 14 } -> { 2 7 } confidence = 7/7 = 100.00% R181: { 2 7 } -> { 14 } confidence = 7/7 = 100.00% R182: { 2 14 } -> { 7 } confidence = 7/7 = 100.00% R183: { 7 14 } -> { 2 } confidence = 7/7 = 100.00%

Lets take L = {2 8 16 } Selected Rules are: R184: { 16 } -> { 2 8 } confidence = 6/6 = 100.00% R185: { 2 16 } -> { 8 } confidence = 6/6 = 100.00% R186: { 8 16 } -> { 2 } confidence = 6/6 = 100.00%

Lets take L = {2 9 18 } Selected Rules are: R187: { 18 } -> { 2 9 } confidence = 5/5 = 100.00% R188: { 2 9 } -> { 18 } confidence = 5/5 = 100.00% R189: { 2 18 } -> { 9 } confidence = 5/5 = 100.00% R190: { 9 18 } -> { 2 } confidence = 5/5 = 100.00%

Lets take L = {2 10 20 } Selected Rules are: R191: { 20 } -> { 2 10 } confidence = 5/5 = 100.00% R192: { 2 20 } -> { 10 } confidence = 5/5 = 100.00% R193: { 10 20 } -> { 2 } confidence = 5/5 = 100.00%

Lets take L = {3 4 6 } Selected Rules are: R194: { 3 4 } -> { 6 } confidence = 8/8 = 100.00% R195: { 4 6 } -> { 3 } confidence = 8/8 = 100.00%

Lets take L = {3 4 12 } Selected Rules are: R196: { 12 } -> { 3 4 } confidence = 8/8 = 100.00% R197: { 3 4 } -> { 12 } confidence = 8/8 = 100.00% R198: { 3 12 } -> { 4 } confidence = 8/8 = 100.00% R199: { 4 12 } -> { 3 } confidence = 8/8 = 100.00%

Lets take L = {3 5 15 } Selected Rules are: R200: { 15 } -> { 3 5 } confidence = 6/6 = 100.00% R201: { 3 5 } -> { 15 } confidence = 6/6 = 100.00% R202: { 3 15 } -> { 5 } confidence = 6/6 = 100.00% R203: { 5 15 } -> { 3 } confidence = 6/6 = 100.00%

Lets take L = {3 6 9 } Selected Rules are: R204: { 6 9 } -> { 3 } confidence = 5/5 = 100.00%

Lets take L = {3 6 12 } Selected Rules are: R205: { 12 } -> { 3 6 } confidence = 8/8 = 100.00% R206: { 3 12 } -> { 6 } confidence = 8/8 = 100.00% R207: { 6 12 } -> { 3 } confidence = 8/8 = 100.00%

Lets take L = {3 6 18 } Selected Rules are: R208: { 18 } -> { 3 6 } confidence = 5/5 = 100.00% R209: { 3 18 } -> { 6 } confidence = 5/5 = 100.00% R210: { 6 18 } -> { 3 } confidence = 5/5 = 100.00%

Lets take L = {3 9 18 } Selected Rules are: R211: { 18 } -> { 3 9 } confidence = 5/5 = 100.00% R212: { 3 18 } -> { 9 } confidence = 5/5 = 100.00% R213: { 9 18 } -> { 3 } confidence = 5/5 = 100.00%

Lets take L = {4 5 10 } Selected Rules are: R214: { 4 5 } -> { 10 } confidence = 5/5 = 100.00% R215: { 4 10 } -> { 5 } confidence = 5/5 = 100.00%

Lets take L = {4 5 20 } Selected Rules are: R216: { 20 } -> { 4 5 } confidence = 5/5 = 100.00% R217: { 4 5 } -> { 20 } confidence = 5/5 = 100.00% R218: { 4 20 } -> { 5 } confidence = 5/5 = 100.00% R219: { 5 20 } -> { 4 } confidence = 5/5 = 100.00%

Lets take L = {4 6 12 } Selected Rules are: R220: { 12 } -> { 4 6 } confidence = 8/8 = 100.00% R221: { 4 6 } -> { 12 } confidence = 8/8 = 100.00% R222: { 4 12 } -> { 6 } confidence = 8/8 = 100.00% R223: { 6 12 } -> { 4 } confidence = 8/8 = 100.00%

Lets take L = {4 8 16 } Selected Rules are: R224: { 16 } -> { 4 8 } confidence = 6/6 = 100.00% R225: { 4 16 } -> { 8 } confidence = 6/6 = 100.00% R226: { 8 16 } -> { 4 } confidence = 6/6 = 100.00%

Lets take L = {4 10 20 } Selected Rules are: R227: { 20 } -> { 4 10 } confidence = 5/5 = 100.00% R228: { 4 10 } -> { 20 } confidence = 5/5 = 100.00% R229: { 4 20 } -> { 10 } confidence = 5/5 = 100.00% R230: { 10 20 } -> { 4 } confidence = 5/5 = 100.00%

Lets take L = {5 10 20 } Selected Rules are: R231: { 20 } -> { 5 10 } confidence = 5/5 = 100.00% R232: { 5 20 } -> { 10 } confidence = 5/5 = 100.00% R233: { 10 20 } -> { 5 } confidence = 5/5 = 100.00%

Lets take L = {6 9 18 } Selected Rules are: R234: { 18 } -> { 6 9 } confidence = 5/5 = 100.00% R235: { 6 9 } -> { 18 } confidence = 5/5 = 100.00% R236: { 6 18 } -> { 9 } confidence = 5/5 = 100.00% R237: { 9 18 } -> { 6 } confidence = 5/5 = 100.00%

Lets take L = {1 2 3 4 } Selected Rules are: R238: { 1 3 4 } -> { 2 } confidence = 8/8 = 100.00% R239: { 2 3 4 } -> { 1 } confidence = 8/8 = 100.00%

Lets take L = {1 2 3 6 } Selected Rules are: R240: { 6 } -> { 1 2 3 } confidence = 16/16 = 100.00% R241: { 1 6 } -> { 2 3 } confidence = 16/16 = 100.00% R242: { 2 3 } -> { 1 6 } confidence = 16/16 = 100.00% R243: { 1 2 3 } -> { 6 } confidence = 16/16 = 100.00% R244: { 1 2 6 } -> { 3 } confidence = 16/16 = 100.00% R245: { 1 3 6 } -> { 2 } confidence = 16/16 = 100.00% R246: { 2 3 6 } -> { 1 } confidence = 16/16 = 100.00%

Lets take L = {1 2 3 9 } Selected Rules are: R247: { 1 2 9 } -> { 3 } confidence = 5/5 = 100.00% R248: { 2 3 9 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 2 3 12 } Selected Rules are: R249: { 12 } -> { 1 2 3 } confidence = 8/8 = 100.00% R250: { 1 12 } -> { 2 3 } confidence = 8/8 = 100.00% R251: { 1 2 12 } -> { 3 } confidence = 8/8 = 100.00% R252: { 1 3 12 } -> { 2 } confidence = 8/8 = 100.00% R253: { 2 3 12 } -> { 1 } confidence = 8/8 = 100.00%

Lets take L = {1 2 3 18 } Selected Rules are: R254: { 18 } -> { 1 2 3 } confidence = 5/5 = 100.00% R255: { 1 18 } -> { 2 3 } confidence = 5/5 = 100.00% R256: { 1 2 18 } -> { 3 } confidence = 5/5 = 100.00% R257: { 1 3 18 } -> { 2 } confidence = 5/5 = 100.00% R258: { 2 3 18 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 2 4 5 } Selected Rules are: R259: { 1 4 5 } -> { 2 } confidence = 5/5 = 100.00% R260: { 2 4 5 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 2 4 6 } Selected Rules are: R261: { 1 4 6 } -> { 2 } confidence = 8/8 = 100.00% R262: { 2 4 6 } -> { 1 } confidence = 8/8 = 100.00%

Lets take L = {1 2 4 8 } Selected Rules are: R263: { 8 } -> { 1 2 4 } confidence = 12/12 = 100.00% R264: { 1 8 } -> { 2 4 } confidence = 12/12 = 100.00% R265: { 1 2 8 } -> { 4 } confidence = 12/12 = 100.00% R266: { 1 4 8 } -> { 2 } confidence = 12/12 = 100.00% R267: { 2 4 8 } -> { 1 } confidence = 12/12 = 100.00%

Lets take L = {1 2 4 10 } Selected Rules are: R268: { 1 4 10 } -> { 2 } confidence = 5/5 = 100.00% R269: { 2 4 10 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 2 4 12 } Selected Rules are: R270: { 12 } -> { 1 2 4 } confidence = 8/8 = 100.00% R271: { 1 12 } -> { 2 4 } confidence = 8/8 = 100.00% R272: { 1 2 12 } -> { 4 } confidence = 8/8 = 100.00% R273: { 1 4 12 } -> { 2 } confidence = 8/8 = 100.00% R274: { 2 4 12 } -> { 1 } confidence = 8/8 = 100.00%

Lets take L = {1 2 4 16 } Selected Rules are: R275: { 16 } -> { 1 2 4 } confidence = 6/6 = 100.00% R276: { 1 16 } -> { 2 4 } confidence = 6/6 = 100.00% R277: { 1 2 16 } -> { 4 } confidence = 6/6 = 100.00% R278: { 1 4 16 } -> { 2 } confidence = 6/6 = 100.00% R279: { 2 4 16 } -> { 1 } confidence = 6/6 = 100.00%

Lets take L = {1 2 4 20 } Selected Rules are: R280: { 20 } -> { 1 2 4 } confidence = 5/5 = 100.00% R281: { 1 20 } -> { 2 4 } confidence = 5/5 = 100.00% R282: { 1 2 20 } -> { 4 } confidence = 5/5 = 100.00% R283: { 1 4 20 } -> { 2 } confidence = 5/5 = 100.00% R284: { 2 4 20 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 2 5 10 } Selected Rules are: R285: { 10 } -> { 1 2 5 } confidence = 10/10 = 100.00% R286: { 1 10 } -> { 2 5 } confidence = 10/10 = 100.00% R287: { 2 5 } -> { 1 10 } confidence = 10/10 = 100.00% R288: { 1 2 5 } -> { 10 } confidence = 10/10 = 100.00% R289: { 1 2 10 } -> { 5 } confidence = 10/10 = 100.00% R290: { 1 5 10 } -> { 2 } confidence = 10/10 = 100.00% R291: { 2 5 10 } -> { 1 } confidence = 10/10 = 100.00%

Lets take L = {1 2 5 20 } Selected Rules are: R292: { 20 } -> { 1 2 5 } confidence = 5/5 = 100.00% R293: { 1 20 } -> { 2 5 } confidence = 5/5 = 100.00% R294: { 1 2 20 } -> { 5 } confidence = 5/5 = 100.00% R295: { 1 5 20 } -> { 2 } confidence = 5/5 = 100.00% R296: { 2 5 20 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 2 6 9 } Selected Rules are: R297: { 1 2 9 } -> { 6 } confidence = 5/5 = 100.00% R298: { 1 6 9 } -> { 2 } confidence = 5/5 = 100.00% R299: { 2 6 9 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 2 6 12 } Selected Rules are: R300: { 12 } -> { 1 2 6 } confidence = 8/8 = 100.00% R301: { 1 12 } -> { 2 6 } confidence = 8/8 = 100.00% R302: { 1 2 12 } -> { 6 } confidence = 8/8 = 100.00% R303: { 1 6 12 } -> { 2 } confidence = 8/8 = 100.00% R304: { 2 6 12 } -> { 1 } confidence = 8/8 = 100.00%

Lets take L = {1 2 6 18 } Selected Rules are: R305: { 18 } -> { 1 2 6 } confidence = 5/5 = 100.00% R306: { 1 18 } -> { 2 6 } confidence = 5/5 = 100.00% R307: { 1 2 18 } -> { 6 } confidence = 5/5 = 100.00% R308: { 1 6 18 } -> { 2 } confidence = 5/5 = 100.00% R309: { 2 6 18 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 2 7 14 } Selected Rules are: R310: { 14 } -> { 1 2 7 } confidence = 7/7 = 100.00% R311: { 1 14 } -> { 2 7 } confidence = 7/7 = 100.00% R312: { 2 7 } -> { 1 14 } confidence = 7/7 = 100.00% R313: { 1 2 7 } -> { 14 } confidence = 7/7 = 100.00% R314: { 1 2 14 } -> { 7 } confidence = 7/7 = 100.00% R315: { 1 7 14 } -> { 2 } confidence = 7/7 = 100.00% R316: { 2 7 14 } -> { 1 } confidence = 7/7 = 100.00%

Lets take L = {1 2 8 16 } Selected Rules are: R317: { 16 } -> { 1 2 8 } confidence = 6/6 = 100.00% R318: { 1 16 } -> { 2 8 } confidence = 6/6 = 100.00% R319: { 1 2 16 } -> { 8 } confidence = 6/6 = 100.00% R320: { 1 8 16 } -> { 2 } confidence = 6/6 = 100.00% R321: { 2 8 16 } -> { 1 } confidence = 6/6 = 100.00%

Lets take L = {1 2 9 18 } Selected Rules are: R322: { 18 } -> { 1 2 9 } confidence = 5/5 = 100.00% R323: { 1 18 } -> { 2 9 } confidence = 5/5 = 100.00% R324: { 2 9 } -> { 1 18 } confidence = 5/5 = 100.00% R325: { 1 2 9 } -> { 18 } confidence = 5/5 = 100.00% R326: { 1 2 18 } -> { 9 } confidence = 5/5 = 100.00% R327: { 1 9 18 } -> { 2 } confidence = 5/5 = 100.00% R328: { 2 9 18 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 2 10 20 } Selected Rules are: R329: { 20 } -> { 1 2 10 } confidence = 5/5 = 100.00% R330: { 1 20 } -> { 2 10 } confidence = 5/5 = 100.00% R331: { 1 2 20 } -> { 10 } confidence = 5/5 = 100.00% R332: { 1 10 20 } -> { 2 } confidence = 5/5 = 100.00% R333: { 2 10 20 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 3 4 6 } Selected Rules are: R334: { 3 4 } -> { 1 6 } confidence = 8/8 = 100.00% R335: { 1 3 4 } -> { 6 } confidence = 8/8 = 100.00% R336: { 1 4 6 } -> { 3 } confidence = 8/8 = 100.00% R337: { 3 4 6 } -> { 1 } confidence = 8/8 = 100.00%

Lets take L = {1 3 4 12 } Selected Rules are: R338: { 12 } -> { 1 3 4 } confidence = 8/8 = 100.00% R339: { 1 12 } -> { 3 4 } confidence = 8/8 = 100.00% R340: { 3 4 } -> { 1 12 } confidence = 8/8 = 100.00% R341: { 1 3 4 } -> { 12 } confidence = 8/8 = 100.00% R342: { 1 3 12 } -> { 4 } confidence = 8/8 = 100.00% R343: { 1 4 12 } -> { 3 } confidence = 8/8 = 100.00% R344: { 3 4 12 } -> { 1 } confidence = 8/8 = 100.00%

Lets take L = {1 3 5 15 } Selected Rules are: R345: { 15 } -> { 1 3 5 } confidence = 6/6 = 100.00% R346: { 1 15 } -> { 3 5 } confidence = 6/6 = 100.00% R347: { 3 5 } -> { 1 15 } confidence = 6/6 = 100.00% R348: { 1 3 5 } -> { 15 } confidence = 6/6 = 100.00% R349: { 1 3 15 } -> { 5 } confidence = 6/6 = 100.00% R350: { 1 5 15 } -> { 3 } confidence = 6/6 = 100.00% R351: { 3 5 15 } -> { 1 } confidence = 6/6 = 100.00%

Lets take L = {1 3 6 9 } Selected Rules are: R352: { 1 6 9 } -> { 3 } confidence = 5/5 = 100.00% R353: { 3 6 9 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 3 6 12 } Selected Rules are: R354: { 12 } -> { 1 3 6 } confidence = 8/8 = 100.00% R355: { 1 12 } -> { 3 6 } confidence = 8/8 = 100.00% R356: { 1 3 12 } -> { 6 } confidence = 8/8 = 100.00% R357: { 1 6 12 } -> { 3 } confidence = 8/8 = 100.00% R358: { 3 6 12 } -> { 1 } confidence = 8/8 = 100.00%

Lets take L = {1 3 6 18 } Selected Rules are: R359: { 18 } -> { 1 3 6 } confidence = 5/5 = 100.00% R360: { 1 18 } -> { 3 6 } confidence = 5/5 = 100.00% R361: { 1 3 18 } -> { 6 } confidence = 5/5 = 100.00% R362: { 1 6 18 } -> { 3 } confidence = 5/5 = 100.00% R363: { 3 6 18 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 3 9 18 } Selected Rules are: R364: { 18 } -> { 1 3 9 } confidence = 5/5 = 100.00% R365: { 1 18 } -> { 3 9 } confidence = 5/5 = 100.00% R366: { 1 3 18 } -> { 9 } confidence = 5/5 = 100.00% R367: { 1 9 18 } -> { 3 } confidence = 5/5 = 100.00% R368: { 3 9 18 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 4 5 10 } Selected Rules are: R369: { 4 5 } -> { 1 10 } confidence = 5/5 = 100.00% R370: { 1 4 5 } -> { 10 } confidence = 5/5 = 100.00% R371: { 1 4 10 } -> { 5 } confidence = 5/5 = 100.00% R372: { 4 5 10 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 4 5 20 } Selected Rules are: R373: { 20 } -> { 1 4 5 } confidence = 5/5 = 100.00% R374: { 1 20 } -> { 4 5 } confidence = 5/5 = 100.00% R375: { 4 5 } -> { 1 20 } confidence = 5/5 = 100.00% R376: { 1 4 5 } -> { 20 } confidence = 5/5 = 100.00% R377: { 1 4 20 } -> { 5 } confidence = 5/5 = 100.00% R378: { 1 5 20 } -> { 4 } confidence = 5/5 = 100.00% R379: { 4 5 20 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 4 6 12 } Selected Rules are: R380: { 12 } -> { 1 4 6 } confidence = 8/8 = 100.00% R381: { 1 12 } -> { 4 6 } confidence = 8/8 = 100.00% R382: { 4 6 } -> { 1 12 } confidence = 8/8 = 100.00% R383: { 1 4 6 } -> { 12 } confidence = 8/8 = 100.00% R384: { 1 4 12 } -> { 6 } confidence = 8/8 = 100.00% R385: { 1 6 12 } -> { 4 } confidence = 8/8 = 100.00% R386: { 4 6 12 } -> { 1 } confidence = 8/8 = 100.00%

Lets take L = {1 4 8 16 } Selected Rules are: R387: { 16 } -> { 1 4 8 } confidence = 6/6 = 100.00% R388: { 1 16 } -> { 4 8 } confidence = 6/6 = 100.00% R389: { 1 4 16 } -> { 8 } confidence = 6/6 = 100.00% R390: { 1 8 16 } -> { 4 } confidence = 6/6 = 100.00% R391: { 4 8 16 } -> { 1 } confidence = 6/6 = 100.00%

Lets take L = {1 4 10 20 } Selected Rules are: R392: { 20 } -> { 1 4 10 } confidence = 5/5 = 100.00% R393: { 1 20 } -> { 4 10 } confidence = 5/5 = 100.00% R394: { 4 10 } -> { 1 20 } confidence = 5/5 = 100.00% R395: { 1 4 10 } -> { 20 } confidence = 5/5 = 100.00% R396: { 1 4 20 } -> { 10 } confidence = 5/5 = 100.00% R397: { 1 10 20 } -> { 4 } confidence = 5/5 = 100.00% R398: { 4 10 20 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 5 10 20 } Selected Rules are: R399: { 20 } -> { 1 5 10 } confidence = 5/5 = 100.00% R400: { 1 20 } -> { 5 10 } confidence = 5/5 = 100.00% R401: { 1 5 20 } -> { 10 } confidence = 5/5 = 100.00% R402: { 1 10 20 } -> { 5 } confidence = 5/5 = 100.00% R403: { 5 10 20 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 6 9 18 } Selected Rules are: R404: { 18 } -> { 1 6 9 } confidence = 5/5 = 100.00% R405: { 1 18 } -> { 6 9 } confidence = 5/5 = 100.00% R406: { 6 9 } -> { 1 18 } confidence = 5/5 = 100.00% R407: { 1 6 9 } -> { 18 } confidence = 5/5 = 100.00% R408: { 1 6 18 } -> { 9 } confidence = 5/5 = 100.00% R409: { 1 9 18 } -> { 6 } confidence = 5/5 = 100.00% R410: { 6 9 18 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {2 3 4 6 } Selected Rules are: R411: { 3 4 } -> { 2 6 } confidence = 8/8 = 100.00% R412: { 2 3 4 } -> { 6 } confidence = 8/8 = 100.00% R413: { 2 4 6 } -> { 3 } confidence = 8/8 = 100.00% R414: { 3 4 6 } -> { 2 } confidence = 8/8 = 100.00%

Lets take L = {2 3 4 12 } Selected Rules are: R415: { 12 } -> { 2 3 4 } confidence = 8/8 = 100.00% R416: { 2 12 } -> { 3 4 } confidence = 8/8 = 100.00% R417: { 3 4 } -> { 2 12 } confidence = 8/8 = 100.00% R418: { 2 3 4 } -> { 12 } confidence = 8/8 = 100.00% R419: { 2 3 12 } -> { 4 } confidence = 8/8 = 100.00% R420: { 2 4 12 } -> { 3 } confidence = 8/8 = 100.00% R421: { 3 4 12 } -> { 2 } confidence = 8/8 = 100.00%

Lets take L = {2 3 6 9 } Selected Rules are: R422: { 2 9 } -> { 3 6 } confidence = 5/5 = 100.00% R423: { 2 3 9 } -> { 6 } confidence = 5/5 = 100.00% R424: { 2 6 9 } -> { 3 } confidence = 5/5 = 100.00% R425: { 3 6 9 } -> { 2 } confidence = 5/5 = 100.00%

Lets take L = {2 3 6 12 } Selected Rules are: R426: { 12 } -> { 2 3 6 } confidence = 8/8 = 100.00% R427: { 2 12 } -> { 3 6 } confidence = 8/8 = 100.00% R428: { 2 3 12 } -> { 6 } confidence = 8/8 = 100.00% R429: { 2 6 12 } -> { 3 } confidence = 8/8 = 100.00% R430: { 3 6 12 } -> { 2 } confidence = 8/8 = 100.00%

Lets take L = {2 3 6 18 } Selected Rules are: R431: { 18 } -> { 2 3 6 } confidence = 5/5 = 100.00% R432: { 2 18 } -> { 3 6 } confidence = 5/5 = 100.00% R433: { 2 3 18 } -> { 6 } confidence = 5/5 = 100.00% R434: { 2 6 18 } -> { 3 } confidence = 5/5 = 100.00% R435: { 3 6 18 } -> { 2 } confidence = 5/5 = 100.00%

Lets take L = {2 3 9 18 } Selected Rules are: R436: { 18 } -> { 2 3 9 } confidence = 5/5 = 100.00% R437: { 2 9 } -> { 3 18 } confidence = 5/5 = 100.00% R438: { 2 18 } -> { 3 9 } confidence = 5/5 = 100.00% R439: { 2 3 9 } -> { 18 } confidence = 5/5 = 100.00% R440: { 2 3 18 } -> { 9 } confidence = 5/5 = 100.00% R441: { 2 9 18 } -> { 3 } confidence = 5/5 = 100.00% R442: { 3 9 18 } -> { 2 } confidence = 5/5 = 100.00%

Lets take L = {2 4 5 10 } Selected Rules are: R443: { 4 5 } -> { 2 10 } confidence = 5/5 = 100.00% R444: { 2 4 5 } -> { 10 } confidence = 5/5 = 100.00% R445: { 2 4 10 } -> { 5 } confidence = 5/5 = 100.00% R446: { 4 5 10 } -> { 2 } confidence = 5/5 = 100.00%

Lets take L = {2 4 5 20 } Selected Rules are: R447: { 20 } -> { 2 4 5 } confidence = 5/5 = 100.00% R448: { 2 20 } -> { 4 5 } confidence = 5/5 = 100.00% R449: { 4 5 } -> { 2 20 } confidence = 5/5 = 100.00% R450: { 2 4 5 } -> { 20 } confidence = 5/5 = 100.00% R451: { 2 4 20 } -> { 5 } confidence = 5/5 = 100.00% R452: { 2 5 20 } -> { 4 } confidence = 5/5 = 100.00% R453: { 4 5 20 } -> { 2 } confidence = 5/5 = 100.00%

Lets take L = {2 4 6 12 } Selected Rules are: R454: { 12 } -> { 2 4 6 } confidence = 8/8 = 100.00% R455: { 2 12 } -> { 4 6 } confidence = 8/8 = 100.00% R456: { 4 6 } -> { 2 12 } confidence = 8/8 = 100.00% R457: { 2 4 6 } -> { 12 } confidence = 8/8 = 100.00% R458: { 2 4 12 } -> { 6 } confidence = 8/8 = 100.00% R459: { 2 6 12 } -> { 4 } confidence = 8/8 = 100.00% R460: { 4 6 12 } -> { 2 } confidence = 8/8 = 100.00%

Lets take L = {2 4 8 16 } Selected Rules are: R461: { 16 } -> { 2 4 8 } confidence = 6/6 = 100.00% R462: { 2 16 } -> { 4 8 } confidence = 6/6 = 100.00% R463: { 2 4 16 } -> { 8 } confidence = 6/6 = 100.00% R464: { 2 8 16 } -> { 4 } confidence = 6/6 = 100.00% R465: { 4 8 16 } -> { 2 } confidence = 6/6 = 100.00%

Lets take L = {2 4 10 20 } Selected Rules are: R466: { 20 } -> { 2 4 10 } confidence = 5/5 = 100.00% R467: { 2 20 } -> { 4 10 } confidence = 5/5 = 100.00% R468: { 4 10 } -> { 2 20 } confidence = 5/5 = 100.00% R469: { 2 4 10 } -> { 20 } confidence = 5/5 = 100.00% R470: { 2 4 20 } -> { 10 } confidence = 5/5 = 100.00% R471: { 2 10 20 } -> { 4 } confidence = 5/5 = 100.00% R472: { 4 10 20 } -> { 2 } confidence = 5/5 = 100.00%

Lets take L = {2 5 10 20 } Selected Rules are: R473: { 20 } -> { 2 5 10 } confidence = 5/5 = 100.00% R474: { 2 20 } -> { 5 10 } confidence = 5/5 = 100.00% R475: { 2 5 20 } -> { 10 } confidence = 5/5 = 100.00% R476: { 2 10 20 } -> { 5 } confidence = 5/5 = 100.00% R477: { 5 10 20 } -> { 2 } confidence = 5/5 = 100.00%

Lets take L = {2 6 9 18 } Selected Rules are: R478: { 18 } -> { 2 6 9 } confidence = 5/5 = 100.00% R479: { 2 9 } -> { 6 18 } confidence = 5/5 = 100.00% R480: { 2 18 } -> { 6 9 } confidence = 5/5 = 100.00% R481: { 6 9 } -> { 2 18 } confidence = 5/5 = 100.00% R482: { 2 6 9 } -> { 18 } confidence = 5/5 = 100.00% R483: { 2 6 18 } -> { 9 } confidence = 5/5 = 100.00% R484: { 2 9 18 } -> { 6 } confidence = 5/5 = 100.00% R485: { 6 9 18 } -> { 2 } confidence = 5/5 = 100.00%

Lets take L = {3 4 6 12 } Selected Rules are: R486: { 12 } -> { 3 4 6 } confidence = 8/8 = 100.00% R487: { 3 4 } -> { 6 12 } confidence = 8/8 = 100.00% R488: { 3 12 } -> { 4 6 } confidence = 8/8 = 100.00% R489: { 4 6 } -> { 3 12 } confidence = 8/8 = 100.00% R490: { 3 4 6 } -> { 12 } confidence = 8/8 = 100.00% R491: { 3 4 12 } -> { 6 } confidence = 8/8 = 100.00% R492: { 3 6 12 } -> { 4 } confidence = 8/8 = 100.00% R493: { 4 6 12 } -> { 3 } confidence = 8/8 = 100.00%

Lets take L = {3 6 9 18 } Selected Rules are: R494: { 18 } -> { 3 6 9 } confidence = 5/5 = 100.00% R495: { 3 18 } -> { 6 9 } confidence = 5/5 = 100.00% R496: { 6 9 } -> { 3 18 } confidence = 5/5 = 100.00% R497: { 3 6 9 } -> { 18 } confidence = 5/5 = 100.00% R498: { 3 6 18 } -> { 9 } confidence = 5/5 = 100.00% R499: { 3 9 18 } -> { 6 } confidence = 5/5 = 100.00% R500: { 6 9 18 } -> { 3 } confidence = 5/5 = 100.00%

Lets take L = {4 5 10 20 } Selected Rules are: R501: { 20 } -> { 4 5 10 } confidence = 5/5 = 100.00% R502: { 4 5 } -> { 10 20 } confidence = 5/5 = 100.00% R503: { 4 10 } -> { 5 20 } confidence = 5/5 = 100.00% R504: { 4 20 } -> { 5 10 } confidence = 5/5 = 100.00% R505: { 4 5 10 } -> { 20 } confidence = 5/5 = 100.00% R506: { 4 5 20 } -> { 10 } confidence = 5/5 = 100.00% R507: { 4 10 20 } -> { 5 } confidence = 5/5 = 100.00% R508: { 5 10 20 } -> { 4 } confidence = 5/5 = 100.00%

Lets take L = {1 2 3 4 6 } Selected Rules are: R509: { 1 3 4 } -> { 2 6 } confidence = 8/8 = 100.00% R510: { 1 2 3 4 } -> { 6 } confidence = 8/8 = 100.00% R511: { 1 2 4 6 } -> { 3 } confidence = 8/8 = 100.00% R512: { 1 3 4 6 } -> { 2 } confidence = 8/8 = 100.00% R513: { 2 3 4 6 } -> { 1 } confidence = 8/8 = 100.00%

Lets take L = {1 2 3 4 12 } Selected Rules are: R514: { 12 } -> { 1 2 3 4 } confidence = 8/8 = 100.00% R515: { 1 12 } -> { 2 3 4 } confidence = 8/8 = 100.00% R516: { 1 2 12 } -> { 3 4 } confidence = 8/8 = 100.00% R517: { 1 3 4 } -> { 2 12 } confidence = 8/8 = 100.00% R518: { 1 3 12 } -> { 2 4 } confidence = 8/8 = 100.00% R519: { 1 2 3 4 } -> { 12 } confidence = 8/8 = 100.00% R520: { 1 2 3 12 } -> { 4 } confidence = 8/8 = 100.00% R521: { 1 2 4 12 } -> { 3 } confidence = 8/8 = 100.00% R522: { 1 3 4 12 } -> { 2 } confidence = 8/8 = 100.00% R523: { 2 3 4 12 } -> { 1 } confidence = 8/8 = 100.00%

Lets take L = {1 2 3 6 9 } Selected Rules are: R524: { 1 2 9 } -> { 3 6 } confidence = 5/5 = 100.00% R525: { 1 2 3 9 } -> { 6 } confidence = 5/5 = 100.00% R526: { 1 2 6 9 } -> { 3 } confidence = 5/5 = 100.00% R527: { 1 3 6 9 } -> { 2 } confidence = 5/5 = 100.00% R528: { 2 3 6 9 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 2 3 6 12 } Selected Rules are: R529: { 12 } -> { 1 2 3 6 } confidence = 8/8 = 100.00% R530: { 1 12 } -> { 2 3 6 } confidence = 8/8 = 100.00% R531: { 1 2 12 } -> { 3 6 } confidence = 8/8 = 100.00% R532: { 1 3 12 } -> { 2 6 } confidence = 8/8 = 100.00% R533: { 1 2 3 12 } -> { 6 } confidence = 8/8 = 100.00% R534: { 1 2 6 12 } -> { 3 } confidence = 8/8 = 100.00% R535: { 1 3 6 12 } -> { 2 } confidence = 8/8 = 100.00% R536: { 2 3 6 12 } -> { 1 } confidence = 8/8 = 100.00%

Lets take L = {1 2 3 6 18 } Selected Rules are: R537: { 18 } -> { 1 2 3 6 } confidence = 5/5 = 100.00% R538: { 1 18 } -> { 2 3 6 } confidence = 5/5 = 100.00% R539: { 1 2 18 } -> { 3 6 } confidence = 5/5 = 100.00% R540: { 1 3 18 } -> { 2 6 } confidence = 5/5 = 100.00% R541: { 1 2 3 18 } -> { 6 } confidence = 5/5 = 100.00% R542: { 1 2 6 18 } -> { 3 } confidence = 5/5 = 100.00% R543: { 1 3 6 18 } -> { 2 } confidence = 5/5 = 100.00% R544: { 2 3 6 18 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 2 3 9 18 } Selected Rules are: R545: { 18 } -> { 1 2 3 9 } confidence = 5/5 = 100.00% R546: { 1 18 } -> { 2 3 9 } confidence = 5/5 = 100.00% R547: { 1 2 9 } -> { 3 18 } confidence = 5/5 = 100.00% R548: { 1 2 18 } -> { 3 9 } confidence = 5/5 = 100.00% R549: { 1 3 18 } -> { 2 9 } confidence = 5/5 = 100.00% R550: { 1 2 3 9 } -> { 18 } confidence = 5/5 = 100.00% R551: { 1 2 3 18 } -> { 9 } confidence = 5/5 = 100.00% R552: { 1 2 9 18 } -> { 3 } confidence = 5/5 = 100.00% R553: { 1 3 9 18 } -> { 2 } confidence = 5/5 = 100.00% R554: { 2 3 9 18 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 2 4 5 10 } Selected Rules are: R555: { 1 4 5 } -> { 2 10 } confidence = 5/5 = 100.00% R556: { 1 4 10 } -> { 2 5 } confidence = 5/5 = 100.00% R557: { 1 2 4 5 } -> { 10 } confidence = 5/5 = 100.00% R558: { 1 2 4 10 } -> { 5 } confidence = 5/5 = 100.00% R559: { 1 4 5 10 } -> { 2 } confidence = 5/5 = 100.00% R560: { 2 4 5 10 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 2 4 5 20 } Selected Rules are: R561: { 20 } -> { 1 2 4 5 } confidence = 5/5 = 100.00% R562: { 1 20 } -> { 2 4 5 } confidence = 5/5 = 100.00% R563: { 1 2 20 } -> { 4 5 } confidence = 5/5 = 100.00% R564: { 1 4 5 } -> { 2 20 } confidence = 5/5 = 100.00% R565: { 1 4 20 } -> { 2 5 } confidence = 5/5 = 100.00% R566: { 1 2 4 5 } -> { 20 } confidence = 5/5 = 100.00% R567: { 1 2 4 20 } -> { 5 } confidence = 5/5 = 100.00% R568: { 1 2 5 20 } -> { 4 } confidence = 5/5 = 100.00% R569: { 1 4 5 20 } -> { 2 } confidence = 5/5 = 100.00% R570: { 2 4 5 20 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 2 4 6 12 } Selected Rules are: R571: { 12 } -> { 1 2 4 6 } confidence = 8/8 = 100.00% R572: { 1 12 } -> { 2 4 6 } confidence = 8/8 = 100.00% R573: { 1 2 12 } -> { 4 6 } confidence = 8/8 = 100.00% R574: { 1 4 6 } -> { 2 12 } confidence = 8/8 = 100.00% R575: { 1 4 12 } -> { 2 6 } confidence = 8/8 = 100.00% R576: { 1 2 4 6 } -> { 12 } confidence = 8/8 = 100.00% R577: { 1 2 4 12 } -> { 6 } confidence = 8/8 = 100.00% R578: { 1 2 6 12 } -> { 4 } confidence = 8/8 = 100.00% R579: { 1 4 6 12 } -> { 2 } confidence = 8/8 = 100.00% R580: { 2 4 6 12 } -> { 1 } confidence = 8/8 = 100.00%

Lets take L = {1 2 4 8 16 } Selected Rules are: R581: { 16 } -> { 1 2 4 8 } confidence = 6/6 = 100.00% R582: { 1 16 } -> { 2 4 8 } confidence = 6/6 = 100.00% R583: { 1 2 16 } -> { 4 8 } confidence = 6/6 = 100.00% R584: { 1 4 16 } -> { 2 8 } confidence = 6/6 = 100.00% R585: { 1 2 4 16 } -> { 8 } confidence = 6/6 = 100.00% R586: { 1 2 8 16 } -> { 4 } confidence = 6/6 = 100.00% R587: { 1 4 8 16 } -> { 2 } confidence = 6/6 = 100.00% R588: { 2 4 8 16 } -> { 1 } confidence = 6/6 = 100.00%

Lets take L = {1 2 4 10 20 } Selected Rules are: R589: { 20 } -> { 1 2 4 10 } confidence = 5/5 = 100.00% R590: { 1 20 } -> { 2 4 10 } confidence = 5/5 = 100.00% R591: { 1 2 20 } -> { 4 10 } confidence = 5/5 = 100.00% R592: { 1 4 10 } -> { 2 20 } confidence = 5/5 = 100.00% R593: { 1 4 20 } -> { 2 10 } confidence = 5/5 = 100.00% R594: { 1 2 4 10 } -> { 20 } confidence = 5/5 = 100.00% R595: { 1 2 4 20 } -> { 10 } confidence = 5/5 = 100.00% R596: { 1 2 10 20 } -> { 4 } confidence = 5/5 = 100.00% R597: { 1 4 10 20 } -> { 2 } confidence = 5/5 = 100.00% R598: { 2 4 10 20 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 2 5 10 20 } Selected Rules are: R599: { 20 } -> { 1 2 5 10 } confidence = 5/5 = 100.00% R600: { 1 20 } -> { 2 5 10 } confidence = 5/5 = 100.00% R601: { 1 2 20 } -> { 5 10 } confidence = 5/5 = 100.00% R602: { 1 5 20 } -> { 2 10 } confidence = 5/5 = 100.00% R603: { 1 2 5 20 } -> { 10 } confidence = 5/5 = 100.00% R604: { 1 2 10 20 } -> { 5 } confidence = 5/5 = 100.00% R605: { 1 5 10 20 } -> { 2 } confidence = 5/5 = 100.00% R606: { 2 5 10 20 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 2 6 9 18 } Selected Rules are: R607: { 18 } -> { 1 2 6 9 } confidence = 5/5 = 100.00% R608: { 1 18 } -> { 2 6 9 } confidence = 5/5 = 100.00% R609: { 1 2 9 } -> { 6 18 } confidence = 5/5 = 100.00% R610: { 1 2 18 } -> { 6 9 } confidence = 5/5 = 100.00% R611: { 1 6 9 } -> { 2 18 } confidence = 5/5 = 100.00% R612: { 1 6 18 } -> { 2 9 } confidence = 5/5 = 100.00% R613: { 1 2 6 9 } -> { 18 } confidence = 5/5 = 100.00% R614: { 1 2 6 18 } -> { 9 } confidence = 5/5 = 100.00% R615: { 1 2 9 18 } -> { 6 } confidence = 5/5 = 100.00% R616: { 1 6 9 18 } -> { 2 } confidence = 5/5 = 100.00% R617: { 2 6 9 18 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 3 4 6 12 } Selected Rules are: R618: { 12 } -> { 1 3 4 6 } confidence = 8/8 = 100.00% R619: { 1 12 } -> { 3 4 6 } confidence = 8/8 = 100.00% R620: { 3 4 } -> { 1 6 12 } confidence = 8/8 = 100.00% R621: { 1 3 4 } -> { 6 12 } confidence = 8/8 = 100.00% R622: { 1 3 12 } -> { 4 6 } confidence = 8/8 = 100.00% R623: { 1 4 6 } -> { 3 12 } confidence = 8/8 = 100.00% R624: { 1 4 12 } -> { 3 6 } confidence = 8/8 = 100.00% R625: { 1 3 4 6 } -> { 12 } confidence = 8/8 = 100.00% R626: { 1 3 4 12 } -> { 6 } confidence = 8/8 = 100.00% R627: { 1 3 6 12 } -> { 4 } confidence = 8/8 = 100.00% R628: { 1 4 6 12 } -> { 3 } confidence = 8/8 = 100.00% R629: { 3 4 6 12 } -> { 1 } confidence = 8/8 = 100.00%

Lets take L = {1 3 6 9 18 } Selected Rules are: R630: { 18 } -> { 1 3 6 9 } confidence = 5/5 = 100.00% R631: { 1 18 } -> { 3 6 9 } confidence = 5/5 = 100.00% R632: { 1 3 18 } -> { 6 9 } confidence = 5/5 = 100.00% R633: { 1 6 9 } -> { 3 18 } confidence = 5/5 = 100.00% R634: { 1 6 18 } -> { 3 9 } confidence = 5/5 = 100.00% R635: { 1 3 6 9 } -> { 18 } confidence = 5/5 = 100.00% R636: { 1 3 6 18 } -> { 9 } confidence = 5/5 = 100.00% R637: { 1 3 9 18 } -> { 6 } confidence = 5/5 = 100.00% R638: { 1 6 9 18 } -> { 3 } confidence = 5/5 = 100.00% R639: { 3 6 9 18 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 4 5 10 20 } Selected Rules are: R640: { 20 } -> { 1 4 5 10 } confidence = 5/5 = 100.00% R641: { 1 20 } -> { 4 5 10 } confidence = 5/5 = 100.00% R642: { 4 5 } -> { 1 10 20 } confidence = 5/5 = 100.00% R643: { 1 4 5 } -> { 10 20 } confidence = 5/5 = 100.00% R644: { 1 4 10 } -> { 5 20 } confidence = 5/5 = 100.00% R645: { 1 4 20 } -> { 5 10 } confidence = 5/5 = 100.00% R646: { 1 5 20 } -> { 4 10 } confidence = 5/5 = 100.00% R647: { 1 4 5 10 } -> { 20 } confidence = 5/5 = 100.00% R648: { 1 4 5 20 } -> { 10 } confidence = 5/5 = 100.00% R649: { 1 4 10 20 } -> { 5 } confidence = 5/5 = 100.00% R650: { 1 5 10 20 } -> { 4 } confidence = 5/5 = 100.00% R651: { 4 5 10 20 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {2 3 4 6 12 } Selected Rules are: R652: { 12 } -> { 2 3 4 6 } confidence = 8/8 = 100.00% R653: { 2 12 } -> { 3 4 6 } confidence = 8/8 = 100.00% R654: { 3 4 } -> { 2 6 12 } confidence = 8/8 = 100.00% R655: { 2 3 4 } -> { 6 12 } confidence = 8/8 = 100.00% R656: { 2 3 12 } -> { 4 6 } confidence = 8/8 = 100.00% R657: { 2 4 6 } -> { 3 12 } confidence = 8/8 = 100.00% R658: { 2 4 12 } -> { 3 6 } confidence = 8/8 = 100.00% R659: { 2 3 4 6 } -> { 12 } confidence = 8/8 = 100.00% R660: { 2 3 4 12 } -> { 6 } confidence = 8/8 = 100.00% R661: { 2 3 6 12 } -> { 4 } confidence = 8/8 = 100.00% R662: { 2 4 6 12 } -> { 3 } confidence = 8/8 = 100.00% R663: { 3 4 6 12 } -> { 2 } confidence = 8/8 = 100.00%

Lets take L = {2 3 6 9 18 } Selected Rules are: R664: { 18 } -> { 2 3 6 9 } confidence = 5/5 = 100.00% R665: { 2 9 } -> { 3 6 18 } confidence = 5/5 = 100.00% R666: { 2 18 } -> { 3 6 9 } confidence = 5/5 = 100.00% R667: { 2 3 9 } -> { 6 18 } confidence = 5/5 = 100.00% R668: { 2 3 18 } -> { 6 9 } confidence = 5/5 = 100.00% R669: { 2 6 9 } -> { 3 18 } confidence = 5/5 = 100.00% R670: { 2 6 18 } -> { 3 9 } confidence = 5/5 = 100.00% R671: { 2 3 6 9 } -> { 18 } confidence = 5/5 = 100.00% R672: { 2 3 6 18 } -> { 9 } confidence = 5/5 = 100.00% R673: { 2 3 9 18 } -> { 6 } confidence = 5/5 = 100.00% R674: { 2 6 9 18 } -> { 3 } confidence = 5/5 = 100.00% R675: { 3 6 9 18 } -> { 2 } confidence = 5/5 = 100.00%

Lets take L = {2 4 5 10 20 } Selected Rules are: R676: { 20 } -> { 2 4 5 10 } confidence = 5/5 = 100.00% R677: { 2 20 } -> { 4 5 10 } confidence = 5/5 = 100.00% R678: { 4 5 } -> { 2 10 20 } confidence = 5/5 = 100.00% R679: { 2 4 5 } -> { 10 20 } confidence = 5/5 = 100.00% R680: { 2 4 10 } -> { 5 20 } confidence = 5/5 = 100.00% R681: { 2 4 20 } -> { 5 10 } confidence = 5/5 = 100.00% R682: { 2 5 20 } -> { 4 10 } confidence = 5/5 = 100.00% R683: { 2 4 5 10 } -> { 20 } confidence = 5/5 = 100.00% R684: { 2 4 5 20 } -> { 10 } confidence = 5/5 = 100.00% R685: { 2 4 10 20 } -> { 5 } confidence = 5/5 = 100.00% R686: { 2 5 10 20 } -> { 4 } confidence = 5/5 = 100.00% R687: { 4 5 10 20 } -> { 2 } confidence = 5/5 = 100.00%

Lets take L = {1 2 3 4 6 12 } Selected Rules are: R688: { 12 } -> { 1 2 3 4 6 } confidence = 8/8 = 100.00% R689: { 1 12 } -> { 2 3 4 6 } confidence = 8/8 = 100.00% R690: { 1 2 12 } -> { 3 4 6 } confidence = 8/8 = 100.00% R691: { 1 3 4 } -> { 2 6 12 } confidence = 8/8 = 100.00% R692: { 1 2 3 4 } -> { 6 12 } confidence = 8/8 = 100.00% R693: { 1 2 3 12 } -> { 4 6 } confidence = 8/8 = 100.00% R694: { 1 2 4 6 } -> { 3 12 } confidence = 8/8 = 100.00% R695: { 1 2 4 12 } -> { 3 6 } confidence = 8/8 = 100.00% R696: { 1 2 6 12 } -> { 3 4 } confidence = 8/8 = 100.00% R697: { 1 2 3 4 6 } -> { 12 } confidence = 8/8 = 100.00% R698: { 1 2 3 4 12 } -> { 6 } confidence = 8/8 = 100.00% R699: { 1 2 3 6 12 } -> { 4 } confidence = 8/8 = 100.00% R700: { 1 2 4 6 12 } -> { 3 } confidence = 8/8 = 100.00% R701: { 1 3 4 6 12 } -> { 2 } confidence = 8/8 = 100.00% R702: { 2 3 4 6 12 } -> { 1 } confidence = 8/8 = 100.00%

Lets take L = {1 2 3 6 9 18 } Selected Rules are: R703: { 18 } -> { 1 2 3 6 9 } confidence = 5/5 = 100.00% R704: { 1 18 } -> { 2 3 6 9 } confidence = 5/5 = 100.00% R705: { 1 2 9 } -> { 3 6 18 } confidence = 5/5 = 100.00% R706: { 1 2 18 } -> { 3 6 9 } confidence = 5/5 = 100.00% R707: { 1 2 3 9 } -> { 6 18 } confidence = 5/5 = 100.00% R708: { 1 2 3 18 } -> { 6 9 } confidence = 5/5 = 100.00% R709: { 1 2 6 9 } -> { 3 18 } confidence = 5/5 = 100.00% R710: { 1 2 6 18 } -> { 3 9 } confidence = 5/5 = 100.00% R711: { 1 2 9 18 } -> { 3 6 } confidence = 5/5 = 100.00% R712: { 1 2 3 6 9 } -> { 18 } confidence = 5/5 = 100.00% R713: { 1 2 3 6 18 } -> { 9 } confidence = 5/5 = 100.00% R714: { 1 2 3 9 18 } -> { 6 } confidence = 5/5 = 100.00% R715: { 1 2 6 9 18 } -> { 3 } confidence = 5/5 = 100.00% R716: { 1 3 6 9 18 } -> { 2 } confidence = 5/5 = 100.00% R717: { 2 3 6 9 18 } -> { 1 } confidence = 5/5 = 100.00%

Lets take L = {1 2 4 5 10 20 } Selected Rules are: R718: { 20 } -> { 1 2 4 5 10 } confidence = 5/5 = 100.00% R719: { 1 20 } -> { 2 4 5 10 } confidence = 5/5 = 100.00% R720: { 1 2 20 } -> { 4 5 10 } confidence = 5/5 = 100.00% R721: { 1 4 5 } -> { 2 10 20 } confidence = 5/5 = 100.00% R722: { 1 4 10 } -> { 2 5 20 } confidence = 5/5 = 100.00% R723: { 1 2 4 5 } -> { 10 20 } confidence = 5/5 = 100.00% R724: { 1 2 4 10 } -> { 5 20 } confidence = 5/5 = 100.00% R725: { 1 2 4 20 } -> { 5 10 } confidence = 5/5 = 100.00% R726: { 1 2 5 20 } -> { 4 10 } confidence = 5/5 = 100.00% R727: { 1 2 10 20 } -> { 4 5 } confidence = 5/5 = 100.00% R728: { 1 2 4 5 10 } -> { 20 } confidence = 5/5 = 100.00% R729: { 1 2 4 5 20 } -> { 10 } confidence = 5/5 = 100.00% R730: { 1 2 4 10 20 } -> { 5 } confidence = 5/5 = 100.00% R731: { 1 2 5 10 20 } -> { 4 } confidence = 5/5 = 100.00% R732: { 1 4 5 10 20 } -> { 2 } confidence = 5/5 = 100.00% R733: { 2 4 5 10 20 } -> { 1 } confidence = 5/5 = 100.00%