4. Let R be a relation defined on Z as follows: For all m, n € Z, m R n iff 4 | (m² — n²). a) Prove that R is an equivalence relation. b) Describe the distinct equivalence classes of the relation R. c) Do the distinct equivalence classes form a partition of Z? Explain.

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Let R be a relation defined on Z as follows: For all m, n € Z, m R n iff 4 | (m² — n²).
a) Prove that R is an equivalence relation.
b) Describe the distinct equivalence classes of the relation R.
c) Do the distinct equivalence classes form a partition of Z? Explain.
Transcribed Image Text:4. Let R be a relation defined on Z as follows: For all m, n € Z, m R n iff 4 | (m² — n²). a) Prove that R is an equivalence relation. b) Describe the distinct equivalence classes of the relation R. c) Do the distinct equivalence classes form a partition of Z? Explain.
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