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3. Let A, B and C be sets. (a) Suppose that ACBand BCC. Does this mean that AC C? Prove your answer. Hint: To prove that ACC you must prove the implication, "for all x, if xEA then xeC."

3. Let A, B and C be sets. (a) Suppose that ACBand BCC. Does this mean that AC C? Prove your answer. Hint: To prove that ACC you must prove the implication, "for all x, if xEA then xeC."

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 87E
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3. Let A, B and C be sets. (a) Suppose that ACBand BC C. Does this mean that AC C? Prove your answer. Hint: To prove that ACC you must prove the implication, "for all x, if xEA then x€C." (b) Suppose that A E B and BE C. Does this mean that A € C? Give an example to prove that this does NOT always happen (and explain why your example works). You should be able to give an example where |A| = |B| = |C| = 2.
Transcribed Image Text:3. Let A, B and C be sets. (a) Suppose that ACBand BC C. Does this mean that AC C? Prove your answer. Hint: To prove that ACC you must prove the implication, "for all x, if xEA then x€C." (b) Suppose that A E B and BE C. Does this mean that A € C? Give an example to prove that this does NOT always happen (and explain why your example works). You should be able to give an example where |A| = |B| = |C| = 2.
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