A relation $R$ is defined on the set $Z$ by “aRb if a – b is divisible by 5” for $a, b \in Z$. Examine if $R$ is a symmetric relation on $Z$.

The correct answer is $R$ is a symmetric relation on $Z$

Let $a, b \in Z$ and aRb hold. Then $a – b$ is divisible by 5 and therefore $b – a$ is divisible by 5.


Thus, aRb $\Rightarrow$ bRa and therefore $R$ is symmetric.