Hi everyone. I've got a one question:

Let M={x belog to P: 1<=x<=500} and X = {x belon to M: 15|x and x|360} where | meand divides.

How to draw a Hasse diagram of the poset (X,|)?

I'll be very appreciate for any advice.

regards

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- Aug 23rd 2009, 11:44 PMSnowboarderHasse diagram
Hi everyone. I've got a one question:

Let M={x belog to P: 1<=x<=500} and X = {x belon to M: 15|x and x|360} where | meand divides.

How to draw a Hasse diagram of the poset (X,|)?

I'll be very appreciate for any advice.

regards - Aug 24th 2009, 08:13 AMnirax
- Aug 24th 2009, 01:23 PMOpalg
First, you need to make a list of all the multiples of 15 that are factors of 360. Since $\displaystyle 360 = 2^3\times3^2\times5$ and $\displaystyle 15=3\times5$, the possible candidates are 15 multiplied by 1, 2, 4 or 8, together with the same numbers multiplied by 3. That gives you the list 15, 30, 60, 120, 45, 90, 180, 360. The Haase diagram then consists of all those numbers, with lines to indicate when one number is a factor of another number. See the attachment.

- Aug 26th 2009, 10:47 PMyoonsi