Solution The smallest relation R1 containing (1, 2) and (2, 3) which is reflexive and
transitive but not symmetric is {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} Now, if we add
the pair (2, 1) to R1 to get R2, then the relation R2 will be reflexive, transitive but not
symmetric 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