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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
 one year ago
 one year 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
 one year ago
 one year ago

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windsylphBest ResponseYou've already chosen the best response.1
I answered Yes for i) and No for ii) by the way
 one year ago

HeroBest ResponseYou've already chosen the best response.1
Did you get this question from a textbook?
 one year ago

windsylphBest ResponseYou've already chosen the best response.1
i rephrased it a little to shorten the question.. is there something wrong with the way I rephrased it?
 one year ago

HeroBest ResponseYou've already chosen the best response.1
Post the question exactly as it is from the book, then post the name, author, and edition of the book.
 one year ago

windsylphBest ResponseYou've already chosen the best response.1
Um, 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
 one year ago

windsylphBest ResponseYou've already chosen the best response.1
I only need parts c and d from the problem in the book by the way
 one year ago

windsylphBest ResponseYou've already chosen the best response.1
Why do you need the author, title, ed, etc of the book?
 one year ago

HeroBest ResponseYou've already chosen the best response.1
To see if I had the book. Hang on
 one year ago

HeroBest ResponseYou've already chosen the best response.1
Which chapter are you working on?
 one year ago

windsylphBest ResponseYou've already chosen the best response.1
9.6, Partial Orderings
 one year ago

HeroBest ResponseYou've already chosen the best response.1
Recall 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.
 one year ago

HeroBest ResponseYou've already chosen the best response.1
Hence, (b) is not a proset either
 one year ago

windsylphBest ResponseYou've already chosen the best response.1
Thank you, but I only need parts c and d, as I've said above :D
 one year ago

HeroBest ResponseYou've already chosen the best response.1
You are correct then, lol
 one year ago

HeroBest ResponseYou've already chosen the best response.1
But you should post a more complete answer than just yes or no
 one year ago

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

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

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

windsylphBest ResponseYou've already chosen the best response.1
Haha that would be my inclination as well. I'm going to ask her again.
 one year ago
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