Answered: 1. Let A, B, and C be subsets of some…

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

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.1: Sets And Geometry

Problem 11E: For the sets gives in Exercise 9, is there a distributive relationship for union with respect with...

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Question

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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