Question

Let A and B be two sets such that n(A) = p and n(B) = q, write the number of functions from A to B.

Answer 1

It is given that A and B are two sets such that n(A) = p and n(B) = q.

Now, any element of set A, say a_i (1 ≤ i ≤ p), is related with an element of set B in q ways. Similarly, other elements of set A are related with an element of set B in q ways.

Thus, every element of set A is related with every element of set B in q ways.

∴ Total number of functions from A to B = q × q × q × ... × q (p times) = q^p