Let A and B be any two sets such that n(A) = p and n(B) = q,

Question:

Let A and B be any two sets such that n(A) = p and n(B) = q, then the total functions from A to B is equal to __________ .

Solution:

n(A) = p, n(B) = q.

here any element of set A, can be connected with elements of B in q ways.

and there are p such elements in A

$\therefore$ Total function possible is $\frac{q \times q \times q \ldots \ldots \times q}{p \text { times }}$

i.e $q^{p}$

$\therefore$ Total functions from $A$ to $B q^{p}$ i.e $n(B)^{n(A)}$.