Question

If $A=1,2,4$ and $B=a,b$ Find the total number of relations from A to B.

Answer 1

Given:$A=\{1,2,4\}$ and $B=\{a,b\}$

Number of relations from $A$ to $B=2^{numberofelementsinA\times B}$

$=2^{numberofelementsinA\times numberofelementsinB}$

$=2^{n\left(A\right)\times n\left(B\right)}$

Number of elements in set $A=3$

Number of elements in set $B=2$

Number of relations from $A$ to $B=2^{n\left(A\right)\times n\left(B\right)}$

$=2^{3\times 2}=2^6=64$