Let X be the set of all subsets of ℤ . Define a relation R on X as follows: Given two subsets of integers A and B , A R B if and only if A ∩ B (complement) = ∅ . Is R an equivalence relation? Prove or disprove.

Let X be the set of all subsets of ℤ . Define a relation R on X as follows: Given two subsets of integers A and B , A R B if and only if A ∩ B (complement) = ∅ . Is R an equivalence relation? Prove or disprove.

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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Let X be the set of all subsets of ℤ . Define a relation R on X as follows: Given two subsets of
integers A and B , A R B if and only if A ∩ B (complement) = ∅ . Is R an equivalence relation? Prove or disprove.

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