Mark the correct alternative in the following question:
Let $A=\{1,2,3\}$ and consider the relation $R=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\}$. Then, $R$ is
(a) reflexive but not symmetric (b) reflexive but not transitive
(c) symmetric and transitive (d) neither symmetric nor transitive
We have,
$R=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\}$
As, $(a, a) \in R \forall a \in A$
So, $R$ is reflexive relation
Also, $(1,2) \in R$ but $(2,1) \notin R$
So, $R$ is not symmetric relation
And, $(1,2) \in R,(2,3) \in R$ and $(1,3) \in R$
So, $R$ is transitive relation
Hence, the correct alternative is option (a).
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