Question

Question 8: Let A = {1,2,3}. Then the number of equivalence relation containing (1.3) is​

Answer 1

Answer:

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.