Question

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​

Answer 1

Step-by-step explanation:

∴R is transitive. Hence, R is an equivalence relation. Now, all elements of the set {1, 3, 5} are related to each other as all the elements of this subset are odd. Thus, the modulus of the difference between any two elements will be even.