Question

Let $A$ and $B$ be two finite sets having $m$ and $n$ elements respectively. Then the total number of mapping from $A$ to $B$ is:

• A. $mn$
• B. $2^{mn}$
• C. $m^n$
• D. $n^m$

Answer 1

Answer: (D)

$n^m$

Consider an element $a\in$A, it can be assigned to any of the $n$ elements of B i.e. it has $n$ images. Similarly each of the $m$ elements of A can have $n$ images in B. Hence, the number of mappings is $n\times n\times n\times$...m times$=$ $n^m$