Let X = {1, 2, 3, 4, 5} and Y = {3, 4}. We define the relation R on the set P (X) by the formula (A R B) ⇔ (A ∪ Y = B ∪ Y). a, Prove that R is an equivalence relation. b, Find [C] for C = {1, 3}. c, How many different equivalence classes of a given relation R exist?

Let X = {1, 2, 3, 4, 5} and Y = {3, 4}. We define the relation R on the set P (X) by the formula (A R B) ⇔ (A ∪ Y = B ∪ Y). a, Prove that R is an equivalence relation. b, Find [C] for C = {1, 3}. c, How many different equivalence classes of a given relation R exist?

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 28E

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Let X = {1, 2, 3, 4, 5} and Y = {3, 4}. We define the relation R on the set P (X) by the formula
(A R B) ⇔ (A ∪ Y = B ∪ Y).

a, Prove that R is an equivalence relation.
b, Find [C] for C = {1, 3}.
c, How many different equivalence classes of a given relation R exist?

The answers to all these questions must be duly substantiated, resp. proven.

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