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Solution


Q.

Let A = {1, 2, 3}. The number of relations on A, containing (1, 2) and (2, 3), which are reflexive and transitive but not symmetric, is __________.          [2025]

Ans.

(3)

For transitive : (1, 2) and (2, 3) ∈ R ⇒ (1, 3) ∈ R

For reflexive : (1, 1), (2, 2), (3, 3) ∈ R

Now, for (2, 1), (3, 2), (3, 1); (3, 1) cannot be taken for not symmetric relation.

Case I : (2, 1) taken and (3, 2) not taken

Case II : (3, 2) taken and (2, 1) not taken

Case III : (2, 1) and (3, 2) are not taken

Therefore, 3 relations are possible.