Thus, R
is transitive Thus, R is an equivalence relation Example 20 Let X = {1, 2, 3, 4, 5, 6, 7, 8, 9} Let R1 be a relation in X given
by R1 = {(x, y) : x – y is divisible by 3} and R2 be another relation on X given by
R2 = {(x, y): {x, y} ⊂ {1, 4, 7}} or {x, y} ⊂ {2, 5, 8} or {x, y} ⊂ {3, 6, 9}}