Consider the following statement. (Assume that all sets are subsets of a universal set U.)For all sets A, B, and C, if ACB and BNC = Ø then ANC = 0.Construct a proof for the statement by selecting sentences from the following scrambled list and putting them in the correct order. Use the element method for proving that a set equals theempty set.Then by definition of intersection and complement A = U.Then (AN C)C = U.Thus BnC ± Ø by definition of Ø.Then x EB because AC B. In addition, we know that x E C.Hence x E Bnby definition of intersection.Therefore A ¢ B.By definition of intersection x E A and xE C.Proof by contradiction:1. Suppose that there exists sets A, B, and C such thatACB, and B nC = Ø and A nC+ Ø.2. Then there exists an element x such that x E AN c.3. --Select-.4. --Select-5. --Select-6. --Select--7. But this contradicts the supposition. Hence the supposition is false, and so A nC = Ø.

Consider the following statement. (Assume that all sets are subsets of a universal set U.) For all sets A, B, and C, if ACB and BnC = 0 then A NC = 0, Construct a proof for the statement by selecting sentences from the following scrambled list and putting them in the correct order. Use the element method for proving that a set equals the empty set. Then by definition of intersection and complement A = U. Then (AN C) = U. Thus BnC + Ø by definition of Ø. Then x E B because AC B. In addition, we know that x E C. Hence x E Bnby definition of intersection. Therefore A ¢ B. By definition of intersection x E A and xE C. Proof by contradiction: 1. Suppose that there exists sets A, B, and C such that ACB, and B NC = Ø and A nc+ Ø. 2. Then there exists an element x such that x € AN c. 3. --Select- 4. --Select- 5. --Select- 6. -Select-- 7. But this contradicts the supposition. Hence the supposition is false, and so AnC = Ø.

Consider the following statement. (Assume that all sets are subsets of a universal set U.) For all sets A, B, and C, if ACB and BnC = 0 then A NC = 0, Construct a proof for the statement by selecting sentences from the following scrambled list and putting them in the correct order. Use the element method for proving that a set equals the empty set. Then by definition of intersection and complement A = U. Then (AN C) = U. Thus BnC + Ø by definition of Ø. Then x E B because AC B. In addition, we know that x E C. Hence x E Bnby definition of intersection. Therefore A ¢ B. By definition of intersection x E A and xE C. Proof by contradiction: 1. Suppose that there exists sets A, B, and C such that ACB, and B NC = Ø and A nc+ Ø. 2. Then there exists an element x such that x € AN c. 3. --Select- 4. --Select- 5. --Select- 6. -Select-- 7. But this contradicts the supposition. Hence the supposition is false, and so AnC = Ø.

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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