I shower every odd day and paint on even ones. Is there a day in which I'm both covered in paint and clean?
You shower every odd day and paint on even ones. So you paint on days 2, 4, 6, 8, etc., and shower on days 1, 3, 5, 7, etc. If you start on day 1 (a shower day), then you will be covered in paint on days 2, 4 and 6 (both even days) but clean on all other days (odd days). Therefore, there is no day when you are both covered in paint and clean at the same time.
Okay that makes sense, thank you for that explanation. However, this could have been accomplished with much less examples and less complicated reasoning. You could have also said that since no even number can be odd and vice versa, there can be no day that you paint and also shower.
You are correct. Even and odd days are mutually exclusive. Thank you for correcting me.