# How l can draw Hasse diagram

How can l draw a Hasse diagram of the divisibility relation, when $$B=\{2,4,5,6,7,10,18,20,24,25\}$$

Would any help, thank you.

• Just connect $a$ and $b$ if $a\mid b$. Do you know which numbers divide which ones? – Dietrich Burde Mar 29 at 19:06
• Start with all the primes at the bottom and build the diagram up connecting those with common divisors like $2$ and $5$ join $10$ and so on. – Yadati Kiran Mar 29 at 19:07
• Yes but I cant draw it because it is partial order relation – Reham Hamdan Mar 29 at 19:10
• Can I draw it by parts beacuse 5 not divisible 2 – Reham Hamdan Mar 29 at 19:14
• Thank you very match Moo – Reham Hamdan Mar 29 at 20:53

$$2,5$$ and $$7$$ are not divisible by any other numbers in the set, so they are on the lowest level. $$4,6$$ and $$10$$ have other numbers ($$18,20$$ and $$24$$) that are multiples of them, so they are intermediate, while $$18,20$$ and $$24$$ are highest. That leaves $$25$$, which is above $$5$$, but not below anything else; it's easiest to draw it on the middle level. After rearranging things on each level to avoid crossing lines, it comes out like this:
$$\begin{array}{ccccccc} 18&&24&&20\\ \huge|&\huge\diagup&\huge|&\huge\diagup&\huge|\\ 6&&4&&10&&25\\ &\huge\diagdown&\huge|&\huge\diagup&\huge|&\huge\diagup\\ 7&&2&&5 \end{array}$$