Give examples of relation which are(i) Neither reflexive nor symmetric nor transitive. (ii) symmetric and reflexive but not transitive.(iii) Reflexive and transitive but not symmetric.

Question

Give examples of relation which are(i) Neither reflexive nor symmetric nor transitive.                (ii) symmetric and reflexive but not transitive.(iii) Reflexive and transitive but not symmetric.

Shiksha Nation · Accepted Answer

Let A = {1, 2, 3}

(i) R = {(1, 1), (2, 3), (3, 1)}

(ii) R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (2, 3), (3, 2)}

(iii) R = {(1, 1), (2, 2), (3, 3), (1, 2)}

Note: - To avoid reflexivity, one of (x, x) should be kept outside of R. To avoid symmetry, take (x, y) ∈R with (y, x) ∉ R. To avoid transitivity, take two pairs (x, y) R and (y , z) ∈ R such that (x, z) ∉ R.

Give examples of relation which are
(i) Neither reflexive nor symmetric nor transitive.
(ii) symmetric and reflexive but not transitive.
(iii) Reflexive and transitive but not symmetric.

Verified Answer