Relational algebra upon schema

[deHasara]

customer=pd.DataFrame({
    'id':[1,2,3,4,5,6,7,8,9],
    'name':['Olivia','Aditya','Cory','Isabell','Dominic','Tyler','Samuel','Daniel','Jeremy'],
    'age':[20,25,15,10,30,65,35,18,23],
    'Product_ID':[101,0,106,0,103,104,0,0,107],
    'Purchased_Product':['Watch','NA','Oil','NA','Shoes','Smartphone','NA','NA','Laptop'],
    'City':['Mumbai','Delhi','Bangalore','Chennai','Chennai','Delhi','Kolkata','Delhi','Mumbai']
})
product=pd.DataFrame({
    'Product_ID':[101,102,103,104,105,106,107],
    'Product_name':['Watch','Bag','Shoes','Smartphone','Books','Oil','Laptop'],
    'Category':['Fashion','Fashion','Fashion','Electronics','Study','Grocery','Electronics'],
    'Price':[299.0,1350.50,2999.0,14999.0,145.0,110.0,79999.0],
    'Seller_City':['Delhi','Mumbai','Chennai','Kolkata','Delhi','Chennai','Bengalore']
})`
pd.merge(product,customer,on='Product_ID')

Need to add this feature(join based on variable)