2. (Problem 4.6) Let A, B be sets. (a) Prove that (b) Prove that P(ANB) P(A) P(B) P(AUB) CP(A) UP(B) (c) Show that in part (b) we have equality iff either ACB or BCA.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.3: Divisibility
Problem 30E: Let be as described in the proof of Theorem. Give a specific example of a positive element of .
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2. (Problem 4.6) Let A, B be sets.
(a) Prove that
(b) Prove that
P(ANB)=P(A)~P(B)
P(AUB) CP(A) UP(B)
(c) Show that in part (b) we have equality iff either ACB or BCA.
Transcribed Image Text:2. (Problem 4.6) Let A, B be sets. (a) Prove that (b) Prove that P(ANB)=P(A)~P(B) P(AUB) CP(A) UP(B) (c) Show that in part (b) we have equality iff either ACB or BCA.
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