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Math Help - Discrete maths poset

  1. #1
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    Discrete maths poset

    Let M = { x \in \mathbb{P}: 1 \leq x \leq 500<br />
}
    and X = { x \in M: 15 |  x and  x | 360}
    (M,|) and (X,|) are posets (recall that a|b means 'a divides b').

    (a) How many maximal elements are in (M,|)?
    (b) List two elements of (M,|) which are incomparable.
    (c) Find |X|.
    (d) Draw a Hasse diagram of the poset (X,|).
    (e) In the poset (M,|) find a totally ordered subset with 9 or more elements.
    ('Totally ordered' refers to the order relation | .)
    (Justify all your answers.)
    thanks

    my answer
    (a) 2
    (d) i know how to draw the graph

    not sure b, c, e. By the way, how to justify them, I'll be very appreciate for any advice.
    Last edited by quah13579; August 27th 2009 at 03:25 AM.
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  2. #2
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    See the answer here.
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  3. #3
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    Quote Originally Posted by Plato View Post
    See the answer here.
    I know how to draw the diagram, can you tell me the others, thanks!
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    any idea how to do (a)(b)(c)(e), please.
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  5. #5
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    Quote Originally Posted by quah13579 View Post
    Let M = { x \in \mathbb{P}: 1 \leq x \leq 500<br />
}
    and X = { x \in M: 15 |  x and  x | 360}
    (M,|) and (X,|) are posets (recall that a|b means 'a divides b').

    (a) How many maximal elements are in (M,|)?
    (b) List two elements of (M,|) which are incomparable.
    (c) Find |X|.
    (d) Draw a Hasse diagram of the poset (X,|).
    (e) In the poset (M,|) find a totally ordered subset with 9 or more elements.
    ('Totally ordered' refers to the order relation | .)
    a) Hint 250 is not maximal but 251 is maximal. WHY?

    b) are 8 & 9 incomparable? WHY?

    If you go to the link I gave you above, you can answer c & d.

    e) \{1,2,4,8,16,32,64,128,256\} works. WHY?
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  6. #6
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    Quote Originally Posted by Plato View Post
    a) Hint 250 is not maximal but 251 is maximal. WHY?

    b) are 8 & 9 incomparable? WHY?

    If you go to the link I gave you above, you can answer c & d.

    e) \{1,2,4,8,16,32,64,128,256\} works. WHY?

    a) i am sorry, it should be 250, not 251 right?
    b) Because 8 can not divide by 9, 9 can not divide by 8
    e) draw a line up to 256.
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