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

c) transitive only

Explanation

A binary relation`{R} `over` Set {X} `is transitive if for all elements a,b,c in {X},

if ` {a} R {b} and {b} R {c}`, then` {a} R {c}`.

A binary relation R over Set X is symmetric

`iff forall a, b in X(a R b leftrightarrow b R a )`

But Given relation is not symmetric

as it contains `(2,3) `but do not contain `(3,2)`.

Since Given relation R contains only one pair` (2,3)`


it is transitive.