CUET Preparation Today
The relation R={(a, b): both a and b are either odd or even} on the set {1, 2, 4, 5, 7, 8} is |
reflexive and symmetric but not transitive reflexive and transitive but not symmetric symmetric and transitive but not reflexive an equivalence relation |
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 |
