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?
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 10E: In Exercises , a relation is defined on the set of all integers. In each case, prove that is an...
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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?
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