Subject: Discrete MathematicsPlease provide answer for LETTER D , E AND F. 7. A, B, and C are subsets of a set S. Prove the following set identities using the basic set identitieslisted in this section. Give a reason for each step. State the dual of each of these identities.a. (A U B) N (A U B') = Ab. ([(A NC) N B] U [(A N C ) N B']) U (A N C )' = Sc. (A U C)N [(A N B) U (C' N B)] = A N Bd. AN (BU A') = BN Aе. (AU B) - C 3D (А- C) U (Bв- с)f. (А- В) - С- (А- C)- В

Introduction: Basic identities of a set: 1. commutative: A∪B=B∪A 2. ASSOCIATIVE: (A∪B)∪C=A∪(B∪C) 3.…

A, B, and C are subsets of a set S. Prove the following set listed in this section. Give a reason for each step. State the a. (A U B) N (A u B') = A b. ([(A NC) N B] U [(A NC) N B']) U (A N C)' = S c. (A UC)n [(A N B) U (C' N B)] = A N B d AO IRU A) = BO A

A, B, and C are subsets of a set S. Prove the following set listed in this section. Give a reason for each step. State the a. (A U B) N (A u B') = A b. ([(A NC) N B] U [(A NC) N B']) U (A N C)' = S c. (A UC)n [(A N B) U (C' N B)] = A N B d AO IRU A) = BO A

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 12E: For the sets given in Exercise 9, is there a distributive relationship for intersection with respect...

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Question

Subject: Discrete Mathematics

Please provide answer for LETTER D , E AND F.

7. A, B, and C are subsets of a set S. Prove the following set identities using the basic set identities
listed in this section. Give a reason for each step. State the dual of each of these identities.
a. (A U B) N (A U B') = A
b. ([(A NC) N B] U [(A N C ) N B']) U (A N C )' = S
c. (A U C)N [(A N B) U (C' N B)] = A N B
d. AN (BU A') = BN A
е. (AU B) - C 3D (А- C) U (Bв- с)
f. (А- В) - С- (А- C)- В

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