The relation R={(a, b): both a and b are either odd or even} on the set {1, 2, 4, 5, 7, 8} is

an equivalence relation

The correct answer is Option (4) → an equivalence relation

(1) R is reflexive

as for ∀ a ∈ set

$(a, a)∈R$ as (a, a) is both odd/even

(2) R is symmetric

if $(a, b)∈R$ ⇒ a, b both odd/even

$⇒(b, a)∈R$

(3) R is transitive

if $(a, b)∈R, (b, c)∈R$ ⇒ a, b, c → all odd/even

$⇒(a, c)∈R$

⇒ equivalence relation