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 | .)

(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.