In 19-31,(1) prove that the relation is an equivalence relation, and (2) describe the distinct equivalence dasses of each relation.
D is the relation defined on Z as follows: For every
(1) The given relation is an equivalence relation,
(2) Describe the distinct equivalence classes of each relation.
D is the relation defined on Z as follows: For all m, n ∈ Z ,
m D n ⇔ 3 | ( m2− n2).
(1). To prove: R is an equivalent relation
A relation will be equivalence relation if it is reflexive, symmetric and transitive.
D is a relation on for
D is symmetric.
So, D is reflexive, symmetric and transitive
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