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5. For any set X, let P(X) denote the power set of X. Prove or disprove the following statements (In other words, determine whether each of the following statements is true or false, and prove your claim. If the statement is true, give a proof. If the statement is false, prove that the negation is true, i.e. give a counterexample). (a) For any sets A and B, P(AN B) = P(A) N P(B). (b) For any sets A and B, P(AU B) = P(A) U P(B). (c) For any sets A, B, and C, A\ (BUC) = (A\ B)U (A \ C). (d) For any sets A, B, C, if An BC C, then (A\C)NB=0.

5. For any set X, let P(X) denote the power set of X. Prove or disprove the following statements (In other words, determine whether each of the following statements is true or false, and prove your claim. If the statement is true, give a proof. If the statement is false, prove that the negation is true, i.e. give a counterexample). (a) For any sets A and B, P(AN B) = P(A) N P(B). (b) For any sets A and B, P(AU B) = P(A) U P(B). (c) For any sets A, B, and C, A\ (BUC) = (A\ B)U (A \ C). (d) For any sets A, B, C, if An BC C, then (A\C)NB=0.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.3: Divisibility
Problem 10TFE
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the last two. With the thinking process， how do u know it is true or not at beginning
5. For any set X, let P(X) denote the power set of X. Prove or disprove the following statements (In other words, determine whether each of the following statements is true or false, and prove your claim. If the statement is true, give a proof. If the statement is false, prove that the negation is true, i.e. give a counterexample). (a) For any sets A and B, P(AN B) = P(A) N P(B). (b) For any sets A and B, P(AU B) = P(A) U P(B). (c) For any sets A, B, and C, A\ (BUC) = (A\ B)U (A \ C). (d) For any sets A, B, C, if An BC C, then (A\C)NB=Ø.
Transcribed Image Text:5. For any set X, let P(X) denote the power set of X. Prove or disprove the following statements (In other words, determine whether each of the following statements is true or false, and prove your claim. If the statement is true, give a proof. If the statement is false, prove that the negation is true, i.e. give a counterexample). (a) For any sets A and B, P(AN B) = P(A) N P(B). (b) For any sets A and B, P(AU B) = P(A) U P(B). (c) For any sets A, B, and C, A\ (BUC) = (A\ B)U (A \ C). (d) For any sets A, B, C, if An BC C, then (A\C)NB=Ø.
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