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Cartesian products 1. Let S = {(1, 2), (1,3), (2, 1), (2,3), (3, 3), (3, 4), (3, 5)}. Give sets A and B so that following two constraints are both satisfied: (1) S C A® B, and (2) |A ® B| is as small as possible. Briefly justify.

Cartesian products 1. Let S = {(1, 2), (1,3), (2, 1), (2,3), (3, 3), (3, 4), (3, 5)}. Give sets A and B so that following two constraints are both satisfied: (1) S C A® B, and (2) |A ® B| is as small as possible. Briefly justify.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Cartesian products 1. Let S = {(1, 2), (1, 3), (2, 1), (2, 3), (3, 3), (3, 4), (3, 5)}. Give sets A and B so that following two constraints are both satisfied: (1) S CA B, and (2) |A ® B| is as small as possible. Briefly justify. 2. Let A be a set. Let D = {(a, a) | a E A} and T = {(a, b) | a, b € A and a + b}. Give a characterization of the set T in terms of some Cartesian product and D. Briefly justify. 3. Beeblebrox writes down the following two expressions as part of his math guide. Explain why both expressions make no sense. (1) (A ® B) \ B and (2) (A ® B)U (A Ð B). (Though there is a contrived version in which the expressions do make sense, but that is surely not what Beeblebrox had in mind.)
Transcribed Image Text:Cartesian products 1. Let S = {(1, 2), (1, 3), (2, 1), (2, 3), (3, 3), (3, 4), (3, 5)}. Give sets A and B so that following two constraints are both satisfied: (1) S CA B, and (2) |A ® B| is as small as possible. Briefly justify. 2. Let A be a set. Let D = {(a, a) | a E A} and T = {(a, b) | a, b € A and a + b}. Give a characterization of the set T in terms of some Cartesian product and D. Briefly justify. 3. Beeblebrox writes down the following two expressions as part of his math guide. Explain why both expressions make no sense. (1) (A ® B) \ B and (2) (A ® B)U (A Ð B). (Though there is a contrived version in which the expressions do make sense, but that is surely not what Beeblebrox had in mind.)
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