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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 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 U C ) N [(A N B) U (C' N B)] = A N B d. AN (BU A') = BN A e. (AU B) - С3 (А- C) U (В-C) f. (А - В) — С%3D (А - С) — В

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 U C ) N [(A N B) U (C' N B)] = A N B d. AN (BU A') = BN A e. (AU B) - С3 (А- C) U (В-C) f. (А - В) — С%3D (А - С) — В

Advanced Engineering Mathematics
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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Discrete Math. Please answer d-f in computerized not written. Thank you!

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. а. (A U B) N (A U B) %3D A b. ([(A N C ) 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 e. (Au B) – C= (A – C) U ( B – C) f. %3D (А - В) — С%3 (А - С) — В
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. а. (A U B) N (A U B) %3D A b. ([(A N C ) 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 e. (Au B) – C= (A – C) U ( B – C) f. %3D (А - В) — С%3 (А - С) — В
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