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

Answer

`R={(1,1),(1,2),(1,3),(2,2),(2,1),(3,3),(3,1)}`

Explanation

`A={1,2,3}`



Relation containing `(1,2) and (1,3)`


For reflexivity, `(1,1),(2,2),(3,3) `must be there in R.


For symmetry,` (1,2),(2,1),(1,3) and (3,1)` must also be in R.
thus ,R is symmetric



For transitive ,`(1,2) in R `but `(2,a) notin R`

`(1,3) in R` but `(3,b) notin R`

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