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 nC)' = S c. (A UC)N [(A N B) U (C' n B)] = ANB d. AN (BU A') = BN A e. (AU B) - C = (A – C) U (B C) f. (A - B) - C = (A – C)– B
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 nC)' = S c. (A UC)N [(A N B) U (C' n B)] = ANB d. AN (BU A') = BN A e. (AU B) - C = (A – C) U (B C) f. (A - B) - C = (A – C)– B
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Subject: Discrete Mathematics
Please provide answer for LETTER A , B AND C.
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb1ee63e-7701-40ae-9009-bd9a5bd390f9%2F86c49afb-c135-4102-a272-2dd0b958444a%2F2kqot9_processed.jpeg&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. (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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