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Let`A = {1, 2, 3}` Then number of relations containing `(1, 2)" and "(1, 3)`which are reflexive and symmetric but not transitive is (A) 1 (B) 2 (C) 3 (D) 4

Answer» Here, `A={1,2,3}`
`R_1={(1,1),(2,2),(3,3)(1,2)(1,3)(2,1)(3,1)(3,2)(2,3)}`
We will work with the relations that contains `(1,2),(3,1)`.
Relation R is reflexive as `(1,1)(2,2)(3,3) in R`
Relation R is symmetric as `(1,2),(2,1) in R` and `(1,3)(3,1) in R`.
Relation R is not transitive since `(3,1)(1,2) in R` but `(3,2) !in R`.
Therefore the total number of relation containing `(1,2)(1,3)` which are reflexive ,symmetric but not transitive is `1`.
However if we add the pair `(3,2)` and `(2,3)` to relation R then it will become transitive.Therefore, the correct answer is 1 (A).


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