Similarly, we can obtain R3 by adding (3, 2) to R1 to get the desired relation However, we can not add two pairs (2, 1), (3, 2) or single pair (3, 1) to R1 at a time, as
by doing so, we will be forced to add the remaining pair in order to maintain transitivity
and in the process, the relation will become symmetric also which is not required Thus,
the total number of desired relations is three Example 24  Show that the number of equivalence relation in the set {1, 2, 3} containing
(1, 2) and (2, 1) is two