Question

If A = {1, 2, 3}, then a relation R = {(2, 3)} on A is

A. symmetric and transitive only
B. symmetric only
C. transitive only
D. none of these

Answer 1

Given relation is R = {(2, 3)}, where A = {1, 2, 3}

∵ 2 ∈ A but (2, 2) ∉ R

∴ R is not a reflexive relation.

Also (2, 3) ∈ R but (3, 2) ∉ R

∴ R is not a symmetric relation.

∵ (2, 3) ∈ R but a ∈ A such that (3, a) ∈ R

Therefore, no requirement that (2, a) ∈ R is exists for R to be a transitive relation.

∴ There is no condition to prove that R is not a transitive relation.

∴ R is a transitive relation.

Answer 2

transitive only (c)