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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb1ee63e-7701-40ae-9009-bd9a5bd390f9%2Faf65fe2d-db16-4ca7-9212-95c1e701200b%2Fjyfc81q_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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