1. ## Discrete maths poset

Let M = {$\displaystyle x \in \mathbb{P}: 1 \leq x \leq 500$}
and X = {$\displaystyle x \in M: 15$ | $\displaystyle x$ and $\displaystyle x$ | 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 | .)
thanks

(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.

3. Originally Posted by Plato
I know how to draw the diagram, can you tell me the others, thanks!

4. any idea how to do (a)(b)(c)(e), please.

5. Originally Posted by quah13579
Let M = {$\displaystyle x \in \mathbb{P}: 1 \leq x \leq 500$}
and X = {$\displaystyle x \in M: 15$ | $\displaystyle x$ and $\displaystyle x$ | 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) $\displaystyle \{1,2,4,8,16,32,64,128,256\}$ works. WHY?

6. Originally Posted by Plato
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) $\displaystyle \{1,2,4,8,16,32,64,128,256\}$ 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.