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. (AUB) (ΑU B ) -Α b. ([(A nC)N B] u [(A n C) N B') U (A N C )' = s c (ΑUC) R [Αn Β) υ ( C B)] -Α Β d. AN (BU A') = BN A e. (AU B) – C = (A – C) U ( B – C) f. (А- В) - С- (А - C) - В
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. (AUB) (ΑU B ) -Α b. ([(A nC)N B] u [(A n C) N B') U (A N C )' = s c (ΑUC) R [Αn Β) υ ( C B)] -Α Β d. AN (BU A') = BN A e. (AU B) – C = (A – C) U ( B – C) f. (А- В) - С- (А - C) - В
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 38E
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Please provide the correct answer for the question stated below:
Answer letter (d-f)
Subject:Discrete Mathematics
![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. (AUB) (ΑU B ) -Α
b. ([(A nC)N B] u [(A n C) N B') U (A N C )' = s
c (ΑUC) R [Αn Β) υ ( C B)] -Α Β
d. AN (BU A') = BN A
e. (AU B) – C = (A – C) U ( B – C)
f. (А- В) - С- (А - C) - В](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F89628c28-3a7a-4c73-9fb0-c43a81427635%2F61fa5de4-23da-4809-b4f1-15d238ae5b7a%2Fgazyaes_processed.png&w=3840&q=75)
Transcribed Image Text: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. (AUB) (ΑU B ) -Α
b. ([(A nC)N B] u [(A n C) N B') U (A N C )' = s
c (ΑUC) R [Αn Β) υ ( C B)] -Α Β
d. AN (BU A') = BN A
e. (AU B) – C = (A – C) U ( B – C)
f. (А- В) - С- (А - C) - В
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