Hasse diagram

**Snowboarder** · August 23rd, 2009, 11:44 PM

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

**nirax** · August 24th, 2009, 08:13 AM

Originally Posted by Snowboarder

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

do you mean Primes by P. if so how can 15 divide a prime number ?

**Opalg** · August 24th, 2009, 01:23 PM

Originally Posted by Snowboarder

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,|)?

First, you need to make a list of all the multiples of 15 that are factors of 360. Since $360 = 2^3\times3^2\times5$ and $15=3\times5$ , 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.