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

Question

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

anonymous · Answer

I answered Yes for i) and No for ii) by the way

hero · Answer

Did you get this question from a textbook?

anonymous · Answer

i rephrased it a little to shorten the question.. is there something wrong with the way I rephrased it?

hero · Answer

Post the question exactly as it is from the book, then post the name, author, and edition of the book.

anonymous · Answer

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

hero · Answer

k

anonymous · Answer

I only need parts c and d from the problem in the book by the way

anonymous · Answer

Why do you need the author, title, ed, etc of the book?

hero · Answer

To see if I had the book. Hang on

anonymous · Answer

Oh okay..

hero · Answer

Which chapter are you working on?

anonymous · Answer

9.6, Partial Orderings

hero · Answer

Standby

hero · Answer

Recall the following: 
A relation, R, on a set A is
(i) Reflexive of (a,a) ∈ R for all a ∈ A
(ii) Anti-symmetric 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, anti-symmetric 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 anti-symmetric 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 · Answer

Hence, (b) is not a proset either

anonymous · Answer

Thank you, but I only need parts c and d, as I've said above :D

hero · Answer

You are correct then, lol

hero · Answer

But you should post a more complete answer than just yes or no

anonymous · Answer

Haha thanks, just want to make sure. My teacher said she doesn't require the actual explanation.

hero · Answer

Yes, but that is the proper way to answer the questions. Yes or No are technically not mathematical responses.

hero · Answer

If I were the teacher, I would tell you that these are not "Yes" or "No" questions.

anonymous · Answer

Haha that would be my inclination as well. I'm going to ask her again.