Rationalised 2023-24
RELATIONS AND FUNCTIONS
5
Solution Given any element a in A, both a and a must be either odd or even, so
that (a, a) ∈ R Further, (a, b) ∈ R ⇒ both a and b must be either odd or even
⇒ (b, a) ∈ R Similarly, (a, b) ∈ R and (b, c) ∈ R ⇒ all elements a, b, c, must be
either even or odd simultaneously ⇒ (a, c) ∈ R Hence, R is an equivalence relation