R is the congruence modulo 7 relation on Z: For all m, n E Z, mRn iff71(m — п).-(i) Is the relation R an equivalence relation? If it is, find the equivalence class of 3.(ii) Prove that R is symmetric.

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R is the congruence modulo 7 relation on Z: For all m, n E Z, mRn iff 7|(m – n). (i) Is the relation R an equivalence relation? If it is, find the equivalence class of 3. (ii) Prove that R is symmetric.

R is the congruence modulo 7 relation on Z: For all m, n E Z, mRn iff 7|(m – n). (i) Is the relation R an equivalence relation? If it is, find the equivalence class of 3. (ii) Prove that R is symmetric.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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R is the congruence modulo 7 relation on Z: For all m, n E Z, mRn iff
71(m — п).
-
(i) Is the relation R an equivalence relation? If it is, find the equivalence class of 3.
(ii) Prove that R is symmetric.

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