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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Transcribed Image Text:8. Let A, B and C be sets.
(a) Suppose that AC B and BC C. Does this mean that A SC? Prove your
answer. 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 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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