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Q.

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

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a

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

b

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

c

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

d

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

answer is C.

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Detailed Solution

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

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Consider the following two binary relations on the set A={a,b,c}:R1={(c,a),(b,b),(a,c),(c,c),(b,c),(a,a)} and R2={(a,b),(b,a),(c,c),(c,a),(a,a),(b,b),(a,c)}Then