Also, A1 coincides with the set of all integers in Z which are related to zero, A2
coincides with the set of all integers which are related to 1 and A3 coincides with the
set of all integers in Z which are related to 2 Thus, A1 = [0], A2 = [1] and A3 = [2] In fact, A1 = [3r], A2 = [3r + 1] and A3 = [3r + 2], for all r ∈ Z 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}