}
Define a relation R in Z given by R = {(a, b) : 3 divides a – b} Following the
arguments similar to those used in Example 5, we can show that R is an equivalence
relation 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]