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Answer the following.
A relation R on the set A = {a, b, c} is defined by R = {(a, b), (b, a)}. Is the relation R…
A relation $R$ on the set $A = \{a, b, c\}$ is defined by $R = \{(a, b), (b, a)\}$. Is the relation $R$ symmetric? Justify.
Answer
Answer
Yes, the relation $R$ is symmetric.
Justification: A relation $R$ is symmetric if for every $(x, y) \in R$, $(y, x) \in R$. Here, $(a, b) \in R$ and its symmetric pair $(b, a) \in R$, and $(b, a) \in R$ with its symmetric pair $(a, b) \in R$. Therefore, $R$ is symmetric.