(a) An (B-C)= (A-C) nB (b) A (B-C) = (A - B) - C (c) (A-B) U (B-A) = (ANB) (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) nÃ) (An (BUB))n((BUB) NA) (ANU)n(UNA) Anà 0 Distributive Law, Difference Equivalence De Morgan's Law, Complementation Law Complement Law (Law of Excluded Middle) (twice) Identity (twice) Complement Law (Contradiction)
(a) An (B-C)= (A-C) nB (b) A (B-C) = (A - B) - C (c) (A-B) U (B-A) = (ANB) (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) nÃ) (An (BUB))n((BUB) NA) (ANU)n(UNA) Anà 0 Distributive Law, Difference Equivalence De Morgan's Law, Complementation Law Complement Law (Law of Excluded Middle) (twice) Identity (twice) Complement Law (Contradiction)
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 10CT: Statement P and Q are true while R is a false statement. Classify as true or false:...
Related questions
Question
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).
Transcribed Image Text:(a) An (B-C) = (A-C) NB
(b) A (B-C) = (A - B) - C
(c) (A-B) U (B-A) = (ANB)
(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 (Bu B))n((BNB)nA)
(An (BUB))n ((BUB) nÃ)
(ANU)n (UnĀ)
AnÃ
0
Distributive Law, Difference Equivalence
De Morgan's Law, Complementation Law
Complement Law (Law of Excluded Middle) (twice)
Identity (twice)
Complement Law (Contradiction)
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