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