Define equivalence relation on a set. Let R be a relation on the set of integers defined by aRb iff a − bis multiple of 5. Prove that R is equivalence relation.

f A={1,4,5} and the relation R defined on the set A as aRb if a+b < 6 checkwhether the relation R is an equivalence relation

Show that R is an equivalence relation, and find all equivalence classes.(a) R = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (1, 5), (5, 1), (3, 5), (5, 3), (1, 3), (3, 1)} on {1, 2, 3, 4, 5}(b) R = {(x, y) : 3 divides (x − y)} on R(c) R = {(x, y) : 3 divides (x + 2y)} on Z(d) R = {(x, y) : x and y are both even} on {1, 2, 3, 4, 5}

Let R be a relation on the set N≥0 given byR = {(a, b) : (b − a) is divisible by 6}Show that this is an equivalence relation

Let R be the relation on the set Z defined by xRy iff x − y is an integer. Prove that R is anequivalence relation on Z.

Suppose a relation R = {(3, 3), (5, 5), (5, 3), (5, 5), (6, 6)} on S = {3, 5, 6}. Here R is known as _________a.equivalence relationb.symmetric relationc.transitive relation’’d.reflexive relat