Please solve the screenshot, thank you! 4. Let S be a set and RC S × S. Given elements a and b of S we say that a is related to b if (a, b) e R.In this case we also write a ~ b.(a) What does it mean that R (or ~) is an equivalence relation.(b) Consider the set of real numbers, S = R. For z, y € R we set z ~ y if z – y e Z, ie., the differenceis an integer. Verify that this defines an equivalence relation.

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Answered: 4. Let S be a set and RC S × S. Given…

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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Please solve the screenshot, thank you!

4. Let S be a set and RC S × S. Given elements a and b of S we say that a is related to b if (a, b) e R.
In this case we also write a ~ b.
(a) What does it mean that R (or ~) is an equivalence relation.
(b) Consider the set of real numbers, S = R. For z, y € R we set z ~ y if z – y e Z, ie., the difference
is an integer. Verify that this defines an equivalence relation.

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Hey, since there are multiple subpart posted, we will answer first 2 questions. If you want any specific question to be answered, then please submit that question only or specify the question number in your message

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We begin with the definition of equivalence relation.

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