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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