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.

  • $\begingroup$ Just connect $a$ and $b$ if $a\mid b$. Do you know which numbers divide which ones? $\endgroup$ – Dietrich Burde Mar 29 at 19:06
  • $\begingroup$ 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. $\endgroup$ – Yadati Kiran Mar 29 at 19:07
  • $\begingroup$ Yes but I cant draw it because it is partial order relation $\endgroup$ – Reham Hamdan Mar 29 at 19:10
  • $\begingroup$ Can I draw it by parts beacuse 5 not divisible 2 $\endgroup$ – Reham Hamdan Mar 29 at 19:14
  • $\begingroup$ Thank you very match Moo $\endgroup$ – 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:

$$ \begin{array}{ccccccc} 18&&24&&20\\ \huge|&\huge\diagup&\huge|&\huge\diagup&\huge|\\ 6&&4&&10&&25\\ &\huge\diagdown&\huge|&\huge\diagup&\huge|&\huge\diagup\\ 7&&2&&5 \end{array} $$


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