Q. 17 Let . Then number of equivalence relations containing  is (A) 1 (B) 2 (C) 3 (D) 4

The number of equivalence relations containing  is given by

We are left with four  pairs  ,, .

, so relation R is reflexive.

and     , so relation R is not symmetric.

, so realation R is not transitive.

Hence , equivalence relation is bigger than R  is universal relation.

Thus the total number of equivalence relations cotaining   is two.

Thus, option B is correct.

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