Let R Be the Relation Defined on the Set of All

question 10

Essay

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.

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