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windsylph

  • 2 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

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  1. windsylph
    • 2 years ago
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    I answered Yes for i) and No for ii) by the way

  2. Hero
    • 2 years ago
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    Did you get this question from a textbook?

  3. windsylph
    • 2 years ago
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    i rephrased it a little to shorten the question.. is there something wrong with the way I rephrased it?

  4. Hero
    • 2 years ago
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    Post the question exactly as it is from the book, then post the name, author, and edition of the book.

  5. windsylph
    • 2 years ago
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    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
    • 2 years ago
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    k

  7. windsylph
    • 2 years ago
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    I only need parts c and d from the problem in the book by the way

  8. windsylph
    • 2 years ago
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    Why do you need the author, title, ed, etc of the book?

  9. Hero
    • 2 years ago
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    To see if I had the book. Hang on

  10. windsylph
    • 2 years ago
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    Oh okay..

  11. Hero
    • 2 years ago
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    Which chapter are you working on?

  12. windsylph
    • 2 years ago
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    9.6, Partial Orderings

  13. Hero
    • 2 years ago
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    Standby

  14. Hero
    • 2 years ago
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    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
    • 2 years ago
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    Hence, (b) is not a proset either

  16. windsylph
    • 2 years ago
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    Thank you, but I only need parts c and d, as I've said above :D

  17. Hero
    • 2 years ago
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    You are correct then, lol

  18. Hero
    • 2 years ago
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    But you should post a more complete answer than just yes or no

  19. windsylph
    • 2 years ago
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    Haha thanks, just want to make sure. My teacher said she doesn't require the actual explanation.

  20. Hero
    • 2 years ago
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    Yes, but that is the proper way to answer the questions. Yes or No are technically not mathematical responses.

  21. Hero
    • 2 years ago
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    If I were the teacher, I would tell you that these are not "Yes" or "No" questions.

  22. windsylph
    • 2 years ago
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    Haha that would be my inclination as well. I'm going to ask her again.

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