Let A be a non-empty funute set and let S = P(A). Define relation R ⊆ S × S by: xRy ⇔ |x| = |y|, where | · | denotes the set cardinality. (i) Prove that R is an equivalence relation. (ii) Find all equivalence classes for the case A = {1, 2, 3}.

Let A be a non-empty funute set and let S = P(A). Define relation R ⊆ S × S by: xRy ⇔ |x| = |y|, where | · | denotes the set cardinality. (i) Prove that R is an equivalence relation. (ii) Find all equivalence classes for the case A = {1, 2, 3}.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...

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Question

Let A be a non-empty funute set and let S = P(A). Define relation R ⊆ S × S by:
xRy ⇔ |x| = |y|,
where | · | denotes the set cardinality.
(i) Prove that R is an equivalence relation.
(ii) Find all equivalence classes for the case A = {1, 2, 3}.

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