Consider the following relation S on the set 1 2 3 4 S 1 22

Consider the following relation S on the set {1, 2, 3, 4}. S = {(1, 2),(2, 2),(3, 2),(4, 2)}. Is this relation reflexive? If not, find the smallest relation S 0 such that S S 0 and S 0 is reflexive. Justify your answer

Solution

A relation is said reflexive if in any of its ordered pair, its both elements are same, it is because reflexive relation is represented as aRa=(a,a) always.

Now here in given relation, we find an ordered pair (2,2) that is of form (a,a), so clearly given relation S is reflexive.