Let X≠ ∅. We define the binary relation R on the potential set P (X) by the formula (A, B) ∈ R ⇔ (A ∩ B) ≠ ∅ Find out whether and under what circumstances this relation is reflexive, symmetric, antisymmetric, transitive. The solution must include the whole process and all the intermediate steps leading to the solution. The answer itself, even if it was right, it is not enough!

Let X≠ ∅. We define the binary relation R on the potential set P (X) by the formula (A, B) ∈ R ⇔ (A ∩ B) ≠ ∅ Find out whether and under what circumstances this relation is reflexive, symmetric, antisymmetric, transitive. The solution must include the whole process and all the intermediate steps leading to the solution. The answer itself, even if it was right, it is not enough!

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 6TFE: Label each of the following statements as either true or false. Let R be a relation on a nonempty...

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