Solution The smallest equivalence relation R1 containing (1, 2) and (2, 1) is {(1, 1),
(2, 2), (3, 3), (1, 2), (2, 1)} Now we are left with only 4 pairs namely (2, 3), (3, 2),
(1, 3) and (3, 1) If we add any one, say (2, 3) to R1, then for symmetry we must add
(3, 2) also and now for transitivity we are forced to add (1, 3) and (3, 1) Thus, the only
equivalence relation bigger than R1 is the universal relation