Let R be the relation deﬁned on the set of all integers Z as follows: for all integers m and n, $$m R n \Longleftrightarrow m - n \text { is divisible by } 5 \text {. }$$
(a) Is R reﬂexive? Prove or give a counterexample.
(b) Is R symmetric? Prove or give a counterexample.
(c) Is R transitive? Prove or give a counterexample.

Question

Let R be the relation deﬁned on the set of all integers Z as follows: for all integers m and n, $$m R n \Longleftrightarrow m - n \text { is divisible by } 5 \text {. }$$ 
(a) Is R reﬂexive? Prove or give a counterexample.
(b) Is R symmetric? Prove or give a counterexample.
(c) Is R transitive? Prove or give a counterexample.

Quizplus · Accepted Answer

The Answer of Let R be the relation deﬁned on the set of all integers Z as follows: for all integers m and n, $$m R n \Longleftrightarrow m - n \text { is divisible by } 5 \text {. }$$ 
(a) Is R reﬂexive? Prove or give a counterexample.
(b) Is R symmetric? Prove or give a counterexample.
(c) Is R transitive? Prove or give a counterexample.

Let R Be the Relation Deﬁned on the Set of All