Question

If the total number of relations from a set A to a set B is $2,$ then find the type of sets A and B.

• A. $A$ is a empty set and $B$ is a singleton set
• B. $B$ is a empty set and $A$ is a singleton set
• C. None of the above
• D. Both $A$ and $B$ is singleton sets

Answer 1

The correct option is D Both $A$ and $B$ is singleton sets

Let, $n\left(A\right)=p$ and $n\left(B\right)=q$

$\therefore$ The total number of relations from A to B is, $2^{pq}$

$\Rightarrow 2^{pq}=2\Rightarrow pq=1\Rightarrow p=1andq=1$

So, $n\left(A\right)=1$ and $n\left(B\right)=1$

Hence, both $A$ and $B$ is singleton sets.