Question

The void relation on a set $A$ is

• A. Reflexive
• B. Symmetric and transitive
• C. Reflexive and symmetric
• D. Reflexive and transitive

Answer 1

The correct option is B

Symmetric and transitive

Explanation of the correct option.

A relation R on set A is known as void or empty relation if no element of a is related to any element of A

That is, $R=\varphi$on set $A\times A$

Let a set $A=\left\{1,3,5\right\}$

And a relation on set $A$ is $R$

$R=\{(a,b):a+b=9\}$

Therefore $(a,b)\notin R$ for any $a,b\in A$

$\therefore$$R$ is an empty set.

$R$ is not reflexive as it does not contain $(a,a)$ for any $a\in R$

Relation $R$ does not contain any element of set $A$. So, relation $R$ will be trivially symmetric and transitive.

Hence option (B) is the correct option.