1. Let A, B, and C be subsets of some universal set U. Prove the following statements from Theorem 4.2.6. (a) AUA = A and AN A= A. (b) AUØ = A and AnØ = 0. (c) ANBCA and A CAUB. %3D

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.2: Mappings
Problem 2TFE: Label each of the following statements as either true or false. 2. for all nonempty sets A and B.
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1. Let A, B, and C be subsets of some universal set U. Prove the following
statements from Theorem 4.2.6.
(a) AUA= A and AN A = A.
(b) AUØ = A and AnØ = 0.
(c) ANBC A and A CAU B.
(d) AU (BUC) = (AU B) U C and An (BnC) = (AN B)NC.
(e) AUB = BUA and AN B = BN A.
(f) AU(BNC) = (AUB) N (AUC).
(g) (AU B) = AnB.
(h) AUĀ=U and AnĀ= 0.
(i) A= A.
ВПА.
Transcribed Image Text:1. Let A, B, and C be subsets of some universal set U. Prove the following statements from Theorem 4.2.6. (a) AUA= A and AN A = A. (b) AUØ = A and AnØ = 0. (c) ANBC A and A CAU B. (d) AU (BUC) = (AU B) U C and An (BnC) = (AN B)NC. (e) AUB = BUA and AN B = BN A. (f) AU(BNC) = (AUB) N (AUC). (g) (AU B) = AnB. (h) AUĀ=U and AnĀ= 0. (i) A= A. ВПА.
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