(15pts) Let A, B and C be sets. Determine whether or not the following are valid. Justify your answer by using either set identities or membership tables. You can also use a counterexample to show that two sets are not equivalent. Notice, that the difference between two sets A and B can be denoted A\B or A-B. A sample solution is provided in part (f). (a) An (B-C) = (A-C) NB (b) A - (B-C) = (A - B) - C (c) (A-B) U (B-A) = (An B) (d) (A-B) U (B-A) = AUB (e) ((A-B) UCU(AUB)) UB=U, where U is the Universal set. (f) ((ANB)u(ANB)) n((BnB) − A) = 0 Solution: The equation is true. We will show this using set identities. ((ANB) u (AnB)) n ((BnB) -A) (An (BUB)) n((BnB) nĀ) (An (BUB)) n((BUB) NA) (ANU)n (UNA) ANĀ 0 Distributive Law, Difference Equivalence De Morgan's Law, Complementation Law Complement Law (Law of Excluded Middle) (twice) Identity (twice) Complement Law (Contradiction)

(15pts) Let A, B and C be sets. Determine whether or not the following are valid. Justify your answer by using either set identities or membership tables. You can also use a counterexample to show that two sets are not equivalent. Notice, that the difference between two sets A and B can be denoted A\B or A-B. A sample solution is provided in part (f). (a) An (B-C) = (A-C) NB (b) A - (B-C) = (A - B) - C (c) (A-B) U (B-A) = (An B) (d) (A-B) U (B-A) = AUB (e) ((A-B) UCU(AUB)) UB=U, where U is the Universal set. (f) ((ANB)u(ANB)) n((BnB) − A) = 0 Solution: The equation is true. We will show this using set identities. ((ANB) u (AnB)) n ((BnB) -A) (An (BUB)) n((BnB) nĀ) (An (BUB)) n((BUB) NA) (ANU)n (UNA) ANĀ 0 Distributive Law, Difference Equivalence De Morgan's Law, Complementation Law Complement Law (Law of Excluded Middle) (twice) Identity (twice) Complement Law (Contradiction)

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.CR: Chapter 12 Review

Problem 4CR

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