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 $n(B)^{n(A)}$.
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