(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)

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
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).

(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)
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) Anà 0 Distributive Law, Difference Equivalence De Morgan's Law, Complementation Law Complement Law (Law of Excluded Middle) (twice) Identity (twice) Complement Law (Contradiction)
Expert Solution
steps

Step by step

Solved in 3 steps with 37 images

Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman