Looking at some exercises in my discrete math book, I came across a few confusing problems.

1) For which sets A, B is it true that A x B = B x A?

2) If there are 2187 functions f: A → B and |B| = 3, what is |A|?

3) Give an example of finite sets A and B with |A|, |B| ≥ 4 and a function f: A→B such that

a) f is neither one-to-one nor onto.