Question

Let $A=\left\{1,2,3\right\}$. The total number of distinct relations that can be defined over $A$ is

• A. $2^9$
• B. $6$
• C. $8$
• D. None of these

Answer 1

The correct option is A

$2^9$

Explanation for correct option:

To find the total number of distinct relations:

Given, $A=\left\{1,2,3\right\}$

The total number of distinct relations between two sets $A$ and $B$ is $2^{pq}$, where $p$,$q$ are the number of elements in set $A$and $B$.

Therefore,

Set $A$ contains $3$ elements , number of distinct elements in relation $A$ over $A$ is $2^{(3\times 3)}=2^9$

Hence, option (A) is the correct answer.