Question

Let $A=\{1,2,3,4\}$ and the relation $R$ on set $A$ is defined as $R=\left\{\right(a,b):a+b=10\}.$ Then $R$ is

• A. a reflexive relation
• B. a symmetric relation
• C. a void relation
• D. a transitive relation

Answer 1

Answer: (B), (C), (D)

a transitive relation

Given $A=\{1,2,3,4\}$
$R=\left\{\right(a,b):a+b=10\}$
Clearly $a+b\ne 10$ for any $a,b\in A$
$\therefore R=\varphi$, which is a void relation.

In this case as $R$ is an empty set there are no elements present in the Relation and no element in A is related to itself.
Hence, void relation is not reflexive.

As the relation is empty the antecedent statement in symmetric and transitive relation is false.
Hence, empty relation is both symmetric and transitive.