R = {(x, e¹x) : x = R, n = Z}.

Let X be the set {1, 2, 3, 4, 5} and Rthe "less than" relation on X, that is x Ryif and only if x

#1. Let R be the relation defined on the set of all integers Z as follows: for all integers m and n, m R n e= m - n is divisible by 5. Prove that R is Equivalence Relation.

Let R be the following relation on the set of real numbers: a Rb→ [a] = [b] , where [æ] is the floor of x. The relation R is: (a) Reflexive, symmetric and antisymmetric (b) Reflexive, symmetric and not antisymmetric (c) Not Reflexive, symmetric and antisymmetric |(d) Reflexive, not symmetric and antisymmetric