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…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 12E: Let and be lines in a plane. Decide in each case whether or not is an equivalence relation, and...

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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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We begin with the definition of equivalence relation.

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