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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."

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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