Question

A relation R on the set A − {a, b, c} is defined by R = {(a, b), (b, a)}. Is the relation R symmetric? Justify.

Answer 1

Given:

A = {a, b, c}

R = {(a, b), (b, a)}

∵ (a, b) ∈ R, we check for (b, a) → (b, a) is present in R.

∵ (b, a) ∈ R, we check for (a, b) → (a, b) present in R.

Since the condition (x, y) ∈ R ⇒ (y, x) ∈ R holds for all pairs in R, the relation is symmetric.