(a) Suppose that A has exactly two elements and B has exactly three. How many different fu...

(a) Suppose that A has exactly two elements and B has exactly three. How many different functions are there from A to B? How many of these are injective? How many are surjective?

(b) Suppose that A has exactly three elements and B has exactly two. How many different functions are there from A to B? How many of these are injective? How many are surjective?

(c) Suppose that A has exactly m elements and B has exactly n elements (where m, n  ε ). How many different functions are there from A to B?