Show that the relation R on the set A={1, 2, 3, 4, 5} given by R={(a,b):`abs(a-b)` is even} in an equivalence ralation.

Show that the relation R on the set A = {1,2,3,4,5) given by R = {(a,b): la -bl is even)} is an equivalence relation. Also, show that all 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).

Show that the relation R is in the set A={1,2,3,4,5} given by R={(a, b): |a-b| is divisible by 2}, is an equivalence relation. Write all the equivalence classes of R.

Show that the relation R on the set Z of integers given by R = {(a,b): 2 divides (a - b)} is an equivalence relation.

Prove that the relation R on the set Z of all integers defined by R={(a, b):a-b is divisible by n} is an equivalence relation.

Let R is the equivalence in the set A = {0, 1, 2, 3, 4, 5} given by R = {(a, b) : 2 divides (a - b)}. Write the equivalence class [0].

If the relation R is defined on the set A={1,2,3,4,5} by R={a,b} : |a^(2)-b^(2)| lt 8 . Then, find the relation R.

State the reason for the relation R in the set {1, 2, 3} given by R ={(1, 2), (2, 1)} not to be transitive.

Show that the relation R on Z – {0} defined by R={(m,n)|frac[m][n] is power of 5} is an equivalence relation.