Question

Check whether the relation R in the set of all vowels defined by R = {(u, u), (u, a), (a, u)} is reflexive, symmetric or transitive?

Answer 1

The relation R is defined in the set {a, e, i, o, u} as R = {(u, u), (u, a), (a, u)}.
The relation R is not reflexive as (a, a), (e, e) (i, i), (o, o) ∉ R.
Now, (u, a) and (a, u) ∈ R
Hence, R is symmetric.
Now, (u, u) (u, a) ∈ R implies (u, a) ∈ R
Also, (u, a), (a, u) ∈ R implies (u, u) ∈ R
Hence, R is transitive.
Thus, the relation R is symmetric and transitive but not reflexive.

Answer 2

the relation of r is symmetric and transitive.