Answered: Let X = {-2, 0, 2} and let P(X) be the…

Let X = {-2, 0, 2} and let P(X) be the power set of x (the set of all subsets of X). A relation U is defined on P(X) as follows: For all S, T ∈ P(X), SUT ⇔ S ⊆ T. Show that U is antisymmetric.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 24E: For any relation on the nonempty set, the inverse of is the relation defined by if and only if ....

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Question

Let X = {-2, 0, 2} and let P(X) be the power set of x (the set of all subsets of X). A relation U is defined on P(X) as follows: For all S, T ∈ P(X), SUT ⇔ S ⊆ T.

Show that U is antisymmetric.

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