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
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 87E
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ques 3 ........ plz send its step by step solution
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F27cdf125-9462-4b4f-84cf-bf07079ff8aa%2Fc529776a-1a4e-4a5b-8493-779ba502f978%2Frlf9d4t_processed.jpeg&w=3840&q=75)
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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