8. Let A, B and C be sets.(a) Suppose that AC B and BC C. Does this mean that A SC? Prove youranswer. Hint: to prove that A CCyou must prove the implication, "for all x, if x €A then x € C."(b) Suppose that A E B and BE C. Does this mean that A € C? Give anexample to prove that this does NOT always happen (and explain why yourexample works). You should be able to give an example where |A| = |B| = |C| = 2.

Answered: Image /qna-images/answer/b6f18cf4-f34e-4ce4-8a27-dac60e2b2466.jpg

8. Let A, B and C be sets. (a) Suppose that AC B and BC C. Does this mean that A S C? Prove your answer. Hint: to prove that A CCyou must prove the implication, "for all x, if x E A then x E C." (b) Suppose that A EB and BE C. Does this mean that A E 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.

8. Let A, B and C be sets. (a) Suppose that AC B and BC C. Does this mean that A S C? Prove your answer. Hint: to prove that A CCyou must prove the implication, "for all x, if x E A then x E C." (b) Suppose that A EB and BE C. Does this mean that A E 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.

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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