Example 6 Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by
R = {(a, b) : both a and b are either odd or even} Show that R is an equivalence
relation 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