Prove the following statements using direct, contrapositive, or proof by-contradiction methods. a. Suppose A, B, and C are sets. Prove that if A is a subset of B, then A - C is a subset of B - C. b. If A, B, and C are sets, then A U (B intersect C) = (A U B) intersect (A U C). c. If A, B and C are sets, then A - (B intersect C) = (A - B) U (A - C). d. If A, B, and C are sets, then A x (B - C) = (A x B) - (A x C). e. Prove that {9^n:n is a rational number} = {3^n:n is a rational number.}

Prove the following statements using direct, contrapositive, or proof by-contradiction methods. a. Suppose A, B, and C are sets. Prove that if A is a subset of B, then A - C is a subset of B - C. b. If A, B, and C are sets, then A U (B intersect C) = (A U B) intersect (A U C). c. If A, B and C are sets, then A - (B intersect C) = (A - B) U (A - C). d. If A, B, and C are sets, then A x (B - C) = (A x B) - (A x C). e. Prove that {9^n:n is a rational number} = {3^n:n is a rational number.}

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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