## 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

1. windsylph

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

2. Hero

Did you get this question from a textbook?

3. windsylph

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

4. Hero

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

5. windsylph

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

6. Hero

k

7. windsylph

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

8. windsylph

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

9. Hero

To see if I had the book. Hang on

10. windsylph

Oh okay..

11. Hero

Which chapter are you working on?

12. windsylph

9.6, Partial Orderings

13. Hero

Standby

14. Hero

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.

15. Hero

Hence, (b) is not a proset either

16. windsylph

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

17. Hero

You are correct then, lol

18. Hero

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

19. windsylph

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

20. Hero

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

21. Hero

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

22. windsylph

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