Let A={1,2,3}. Then, the number of relation containing (1,2) and (1,3) which are reflexive and symmetric but not transitive is
(a)1
(b)2
(c)3
(d)4

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Solution

Relation R is reflexive as $(1, 1), (2, 2), (3, 3) \in R .$ Relations R is symmetric since $(1, 2), (2, 1) \in R a n d (1, 3), (3, 1) \in R .$
But relation R is not transitive as $(3, 1), (1, 2) \in R b u t (3, 2) / \in R .$
Now, if we add any one of the two pairs (3,2)and (2,3)(or both) to relation R, then relation R will become transitive.
Hence, the total number of desired relations is one.
Thus, the correct answer is (a).

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