Let R be a relation on the integers, where R=

Let R = , where N is the set of all natural numbers. Then the relation R is :

Let R be a relation on the set N of natural numbers defined by nRm Û n is a factor of m (i.e., n|m). Then R is

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.

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.

Let R be the relation on Z≥ (the set of integers) defined by (x, y) ∈ R iff x2 + y2 = 2k for some integers k ≥0.Which one of the following is an ordered pair in R?a.(1, 0)b.(2, 9)c.(3, 8)d.(5, 7)