Consider the following two binary relations on the set $A {a, b, c}$
$R_{1} {(c, a), (b, b), (a, c), (b, c), (a, a)} R_{2} {(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)}$ Then

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Both $R_{1}$ and $R_{2}$ are not symmetric

$R_{1}$ is not symmetric but it is transitive

Both $R_{1}$ and $R_{2}$ are transitive

$R_{2}$ is symmetric but it is not transitive

answer is A.

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Detailed Solution

$(b, c) \in R_{1}$ but $(c, b) \in R_{1}$    $∴ R_{1}$ is not symmetric
$(b, c) \in R_{1}$ but $(c, a) \in R_{1}$    $∴ R_{1}$ is not transitive $∴ R_{2}$ is symmetric
$(b, a) \in R_{2}$ but $(a, c) \in R_{2}$ but $(b, c) \in R_{2}$    $∴ R_{2}$ is not transitive