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
Related questions
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa9868944-314b-465d-88a0-68e22c5aecd4%2F04c5a08d-659e-40b5-b2cc-8697da9835c3%2Ftig9bdv_processed.png&w=3840&q=75)
Transcribed Image Text: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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