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 __________ .

Answer 1

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 $\frac{q\times q\times q.......\times q}{p\mathrm{times}}$
i.e q^p

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