Consider the following relation S on the set 1 23 4 S 1 2 2

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\' such that S subset S\' and S\' is reflexive.

Solution

Reflexive is true means all elements should have relation with itself.

Here 1 is not related to 1 and 3 not related to 3 and 4 also not related to 4

Hence S is not reflexive.

Smallest relation for reflexive is atleast (1,1) (3,3) (4,4) should be added to S

Thus S\'= {(1,1) (3,3) (4,4),(1,2)(2,2)(3,2)(4,2) }

Block letters represent new elements added to make S reflexive.