Question

The number of relations from $A=\{2,6\}$to $B=\{1,3,5,7\}$ that are not functions from $A$ to $B$ is

• A. $240$
• B. $16$
• C. $128$
• D. $200$

Answer 1

The correct option is A $240$

If both sets $A$ and $B$ have $m$ and $n$ number of elements respectively, then,
Number of relations from set $A$ to set $B=2^{mn}=2^{2\times 4}=2^8=256$
Number of functions from set $A$ to set $B=n^m=4^2=16$
$\therefore$ Number of relations that are not functions from set $A$ to set $B$
$=256-16=240$