Further, show that all the elements of the subset {1, 3, 5, 7} are related to each
other and all the elements of the subset {2, 4, 6} are related to each other, but no
element of the subset {1, 3, 5, 7} is related to any element of the subset {2, 4, 6} 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