Suppose $R$ is a relation on a set $A$ where $A$ = {a, b, c} and R = {(a, a), (a, b), (a, c), (b, c), (c, a)}. Determine the elements which should be in R to make R a symmetric relation.

The correct answer is (b, a) and (c, b)

To make $R$ a symmetric relation, we need to check for each element in $R$.

(a, a) $\in R$ ⇒ (a, a) $\in R$

(a, b) $\in R$ ⇒ (b, a) $\in R$, but (b, a) $\notin R$

(a, c) $\in R$ ⇒ (c, a) $\in R$

(b, c) $\in R$ ⇒ (c, b) $\in R$, but (c, b) $\notin R$


Hence, (b, a) and (c, b) should belong to $R$ to make $R$ a symmetric relation.