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windsylph
 3 years ago
Let S be the set of all people in the world, a and b be people in S, and R be the relation given in each item below. Is (S,R) a partially ordered set?
i) a = b or a is a descendant of b
ii) a and be do NOT have a common friend
windsylph
 3 years ago
Let S be the set of all people in the world, a and b be people in S, and R be the relation given in each item below. Is (S,R) a partially ordered set? i) a = b or a is a descendant of b ii) a and be do NOT have a common friend

This Question is Closed

windsylph
 3 years ago
Best ResponseYou've already chosen the best response.1I answered Yes for i) and No for ii) by the way

Hero
 3 years ago
Best ResponseYou've already chosen the best response.1Did you get this question from a textbook?

windsylph
 3 years ago
Best ResponseYou've already chosen the best response.1i rephrased it a little to shorten the question.. is there something wrong with the way I rephrased it?

Hero
 3 years ago
Best ResponseYou've already chosen the best response.1Post the question exactly as it is from the book, then post the name, author, and edition of the book.

windsylph
 3 years ago
Best ResponseYou've already chosen the best response.1Um, okay, this is from Kenneth Rosen's Discrete Mathematics and Its Applications, 7th ed. Here's a screenshot from the book too: https://dl.dropbox.com/u/17638088/prob.PNG

windsylph
 3 years ago
Best ResponseYou've already chosen the best response.1I only need parts c and d from the problem in the book by the way

windsylph
 3 years ago
Best ResponseYou've already chosen the best response.1Why do you need the author, title, ed, etc of the book?

Hero
 3 years ago
Best ResponseYou've already chosen the best response.1To see if I had the book. Hang on

Hero
 3 years ago
Best ResponseYou've already chosen the best response.1Which chapter are you working on?

windsylph
 3 years ago
Best ResponseYou've already chosen the best response.19.6, Partial Orderings

Hero
 3 years ago
Best ResponseYou've already chosen the best response.1Recall the following: A relation, R, on a set A is (i) Reflexive of (a,a) ∈ R for all a ∈ A (ii) Antisymmetric if (a,b),(b,a)∈R implies that a = b (iii) Transitive if (a,b),(b,c) ∈ R implies that (a,c)∈ R (iv) A partial ordering if it is reflexive, antisymmetric and transitive. Suppose S is the set of all people in the world: (a) R = {(a,b) ∈ R  a is no shorter than b} is a relation on S. Then, R is not antisymmetric because there may be two different persons with the same height. Hence, (S,R) is not a proset. (b) R = {(a,b) ∈ R  a weighs more than b} is a relation on S. Then R is not reflexive because no other person weighs more than him or herself.

Hero
 3 years ago
Best ResponseYou've already chosen the best response.1Hence, (b) is not a proset either

windsylph
 3 years ago
Best ResponseYou've already chosen the best response.1Thank you, but I only need parts c and d, as I've said above :D

Hero
 3 years ago
Best ResponseYou've already chosen the best response.1But you should post a more complete answer than just yes or no

windsylph
 3 years ago
Best ResponseYou've already chosen the best response.1Haha thanks, just want to make sure. My teacher said she doesn't require the actual explanation.

Hero
 3 years ago
Best ResponseYou've already chosen the best response.1Yes, but that is the proper way to answer the questions. Yes or No are technically not mathematical responses.

Hero
 3 years ago
Best ResponseYou've already chosen the best response.1If I were the teacher, I would tell you that these are not "Yes" or "No" questions.

windsylph
 3 years ago
Best ResponseYou've already chosen the best response.1Haha that would be my inclination as well. I'm going to ask her again.
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