Question:
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:
Given set is {1,2,3}
Let the relation is R.
Now
R is reflexive if (1,1),(2,2)(3,3) ∈ R
R is symmetric if (1,2), (2,1) ∈ R and (1,3),(3,1) ∈ R
R is not transitive as (3,1),(1,2) ∈ R but (3,2) ∈ R
Now if we add either (3,2) or (2,3) in R then R will become a transitive relation.
So total number of desired relation is one
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