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Problem 4 from Section 4.1: "Let, A, B, C be sets. Write the following in “if... then" format and prove: (a) x EB is a sufficient condition for x € AUB. (b) An BnC=0 is a necessary condition for AnB = 0. (c) AUB=B is a necessary and sufficient condition for ACB."

Problem 4 from Section 4.1: "Let, A, B, C be sets. Write the following in “if... then" format and prove: (a) x EB is a sufficient condition for x € AUB. (b) An BnC=0 is a necessary condition for AnB = 0. (c) AUB=B is a necessary and sufficient condition for ACB."

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 40E
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(1) Problem 4 from Section 4.1: "Let, A, B, C be sets. Write the following in "if... then" format and prove: (a) x B is a sufficient condition for x € AUB. An BnC = 0) is a necessary condition for AnB = 0. (c) AUB = B is a necessary and sufficient condition for AC B."
Transcribed Image Text:(1) Problem 4 from Section 4.1: "Let, A, B, C be sets. Write the following in "if... then" format and prove: (a) x B is a sufficient condition for x € AUB. An BnC = 0) is a necessary condition for AnB = 0. (c) AUB = B is a necessary and sufficient condition for AC B."
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