Question 8

Show that the relation R in the set A = {1, 2, 3, 4, 5} given by R = {( a, b) : | a - b| is even}, is an equivalence relation. Show that all the elements of {1, 3, 5} are related to each other and all the elements of {2, 4} are related to each other. But no element of {1, 3, 5} is related to any element of {2, 4}.