Question

Let $R=\left\{(a,a)\right\}$ be a relation on set $A$.Then $R$ is

• A. Symmetric
• B. Antisymmetric
• C. Symmetric and antisymmetric
• D. Neither symmetric nor antisymmetric

Answer 1

The correct option is C

Symmetric and antisymmetric

Explanation for the correct option:

Checking if $\mathit{R}$ is symmetric and antisymmetric:

suppose $(a,b)\in R$this means $a=b$ hence $(b,a)\in R$

Hence $R$ is symmetric

suppose $(a,b)\in R$ and $\left(b,a\right)\in R$

then $a=b$ since $(a,b)\in R$

Hence by definition of antisymmetric relation

$R$ is antisymmetric

Hence option(C) is the correct answer