2.Suppose A = {1, 2, 3, 4, · .. , 14, 15} and let R be the relation of congruence modulo5 on the set A denoted byI = y (mod 5) .This mean that the difference xy is divisible by 5.(a) Show that R is an equivalence relation on A.(b) Find the quotient set A/R.

Answered: Image /qna-images/answer/5c6e7b17-9e1e-4bb2-a457-c4e277dc39a7.jpg

Answered: 2. Suppose A = {1, 2, 3, 4, .. , 14,…

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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2. Suppose A = {1, 2, 3, 4, .. , 14, 15} and let R be the relation of congruence modulo 5 on the set A denoted by I = y (mod 5) . This mean that the difference x - y is divisible by 5. (a) Show that R is an equivalence relation on A. (b) Find the quotient set A/R.