2. Let A = {2,4,6,8}. Suppose B is a set with |B| = 5.(a) What are the smallest and largest possible values of JA U B|? Explain.(b) What are the smallest and largest possible values of |A O B|? Explain.(c) What are the smallest and largest possible values of |A × B|? Explain.3. Let A, B and C be sets.(a) Suppose that ACB and BC C. Does this mean that A C C? Prove your answer. Hint: Toprove that ACC you must prove the implication, “for all x, if xEA then x€C."(b) Suppose that A E B and B e C. Does this mean that A € C? Give an example to prove thatthis does NOT always happen (and explain why your example works). You should be able togive an example where |A| = |B| = |C| = 2.

2) We have given that , A = 2 , 4 , 6 , 8 Here , A = 4 , B = 5 (a) We need to find largest and…

2. Let A = {2,4,6,8}. Suppose B is a set with |B| = 5. (a) What are the smallest and largest possible values of |A U B|? Explain. (b) What are the smallest and largest possible values of JA n B|? Explain. (c) What are the smallest and largest possible values of |A × B|? Explain. 3. Let A, B and C be sets. (a) Suppose that AS B and BS C. Does this mean that A S C? Prove your answer. Hint: To prove that ACC you must prove the implication, "for all x, if x€A then x€C." (b) Suppose that A € B and B e 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.

2. Let A = {2,4,6,8}. Suppose B is a set with |B| = 5. (a) What are the smallest and largest possible values of |A U B|? Explain. (b) What are the smallest and largest possible values of JA n B|? Explain. (c) What are the smallest and largest possible values of |A × B|? Explain. 3. Let A, B and C be sets. (a) Suppose that AS B and BS C. Does this mean that A S C? Prove your answer. Hint: To prove that ACC you must prove the implication, "for all x, if x€A then x€C." (b) Suppose that A € B and B e 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.

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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Question

2. Let A = {2,4,6,8}. Suppose B is a set with |B| = 5.
(a) What are the smallest and largest possible values of JA U B|? Explain.
(b) What are the smallest and largest possible values of |A O B|? Explain.
(c) What are the smallest and largest possible values of |A × B|? Explain.
3. Let A, B and C be sets.
(a) Suppose that ACB and BC C. Does this mean that A C 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 B e 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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