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
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.1: Sets And Geometry
Problem 12E: For the sets given in Exercise 9, is there a distributive relationship for intersection with respect...
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff3ba02c-c8c1-4343-b00d-db81c54b10e9%2Fbdb34423-8456-4a9b-ad8a-1c642b6ed238%2Fl9mluv_processed.png&w=3840&q=75)
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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