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Let A be a nonempty set and B be a fixed subset of A. Define R to be the relation on P(A) such that (VS,TE P(A)) SRT iff SnB = TnB. 1. Show that is an equivalence relation on (A). 2. Set A = {1, 2, 3, 4} and B = {1, 2,4}. Determine [S], for S = {2,3,4}.

Let A be a nonempty set and B be a fixed subset of A. Define R to be the relation on P(A) such that (VS,TE P(A)) SRT iff SnB = TnB. 1. Show that is an equivalence relation on (A). 2. Set A = {1, 2, 3, 4} and B = {1, 2,4}. Determine [S], for S = {2,3,4}.

Elements Of Modern Algebra
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 A be a nonempty set and B be a fixed subset of A. Define to be the relation on P(A) such that (VS,TE P(A)) SRT iff SnB = TnB. 1. Show that is an equivalence relation on (A). 2. Set A = {1, 2, 3, 4) and B = {1, 2, 4}. Determine [S], for S = {2, 3,4}
Transcribed Image Text:Let A be a nonempty set and B be a fixed subset of A. Define to be the relation on P(A) such that (VS,TE P(A)) SRT iff SnB = TnB. 1. Show that is an equivalence relation on (A). 2. Set A = {1, 2, 3, 4) and B = {1, 2, 4}. Determine [S], for S = {2, 3,4}
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