Question

Let $A=\{a,b,c,d,e\}$ and $B=\{1,2,3,4,5\}$. The number of relations which are not functions from $A$ to $B$ is

• A. $2^{25}-5^5$
• B. $2^{20}-5^5$
• C. $5^5-25$
• D. $2^{25}-5\times 3$

Answer 1

The correct option is A $2^{25}-5^5$

$n\left(A\right)=5,n\left(B\right)=5$
$n(A\times B)=5\times 5=25$
$\therefore$ Total number of relations from $A$ to $B$ is,
$2^{n(A\times B)}=2^{25}$
Now, total number of functions from $A$ to $B$ is $5^5$
Hence, the number of relations which are not functions
$=2^{25}-5^5$