Question

Let $A$ and $B$ be finite sets such that $n(A)=3$ . If the total number of relations that can be defined from $A$ to $B$ is $4096$ , then $n(B)=$

• A. $5$
• B. $4$
• C. $6$
• D. $8$

Answer 1

Answer: (B)

Let the number of elements in set $B$ be $x$.
Number of elements in set $A=3$
Number of relations from $A$ to $B=4096$
$\Rightarrow 2^{3x}=4096$
$\Rightarrow 2^{3x}=2^{12}$
On comparing, we get $3x=12\Rightarrow x=4$
So, number of elements in set $B=4$