Question

Let A = {1, 2, 3}. Then number of equivalence relations containing (1, 2) is

(A) 1    (B)   2   (C) 3   (D) 4

Answer 1

If we odd any one pair [say (2, 3)] to R1, then for symmetry we must add (3, 2). Also, for transitivity we are required to add (1, 3) and (3, 1). Hence, the only equivalence relation (bigger than R₁) is the universal relation.
This shows that the total number of equivalence relations containing (1, 2) is two.
The correct answer is B.