5. Let R be a relation from the power set P(X) to itself, where X = {1,2,3, 4}, defined by A R B if A C B. a. Is A RA for all A E P(X)? Explain or give a counter-example. b. For any A, B E P(X), if A R B, is B R A? Explain or give a counter-example.
5. Let R be a relation from the power set P(X) to itself, where X = {1,2,3, 4}, defined by A R B if A C B. a. Is A RA for all A E P(X)? Explain or give a counter-example. b. For any A, B E P(X), if A R B, is B R A? Explain or give a counter-example.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 14E: In each of the following parts, a relation is defined on the set of all human beings. Determine...
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Please help with question 5. Thank you.
Transcribed Image Text:5. Let R be a relation from the power set P(X) to itself, where X = {1,2,3, 4}, defined by A R B
if A C B.
a. Is A RA for all A E P(X)? Explain or give a counter-example.
b. For any A, B e P(X), if A R B, is B R A? Explain or give a counter-example.
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