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
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
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
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Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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 ∪ B) ∩ (A ∪ B′) = A
b. ([(A ∩ C ) ∩ B] ∪ [(A ∩ C ) ∩ B′]) ∪ (A ∩ C )′ = S
c. (A ∪ C ) ∩ [(A ∩ B) ∪ (C′ ∩ B)] = A ∩ B
d. A ∩ (B ∪ A′) = B ∩ A
e. (A ∪ B) − C = (A − C ) ∪ ( 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 N C) n B] U [(A N C ) N B']) U (A N C )' = S
c. (A UC) N [(A N B) U (C' O B)] = A N B
d. AN (BU A') = BN A
e. (AU B) - C = (A – C) U ( B- C)
f. (A - B) - C = (A – C) – B](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbc7b427e-4ba6-4b07-b21c-400e60219e5b%2F0e2a603a-88eb-4c0a-a67d-44dbf7a54719%2Ff402rfe_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 N C) n B] U [(A N C ) N B']) U (A N C )' = S
c. (A UC) N [(A N B) U (C' O B)] = A N B
d. AN (BU A') = BN A
e. (AU B) - C = (A – C) U ( B- C)
f. (A - B) - C = (A – C) – B
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