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I am trying to draw a Hasse diagram and wanted to see if anyone can let me know if I am doing it right.

Let R = {(a,b) | a divides b} be a relation over the set {1, 2, 3, 4, 5, 12}

That is what I have so far and I'm not sure if it is the right diagram.

The maximal element of R would be 12 and 5, 12 is the greatest element

The minimal element of R would be 1, it is also the least element

The least upper bound of {2} is 4.

Is this right?

Thank you for your time

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The diagram looks right.

But I don't agree with "the least upper bound of $\{2\}$ is $4$". Namely, $2$ is another, smaller upper bound.

Also, under the "divides" relation, 12 and 5 are incomparable, so neither of them can be a greatest element.

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  • $\begingroup$ So there isn't a greatest element and the least upper bound of {2} is 2? $\endgroup$ – Karim B Apr 3 '15 at 0:54
  • $\begingroup$ @KarimB: Correct. In general, a one-element set always has the element itself as least upper bound as well as greatest lower bound. $\endgroup$ – Henning Makholm Apr 3 '15 at 1:02
  • $\begingroup$ Thank you so much for clearing that up! $\endgroup$ – Karim B Apr 3 '15 at 1:45

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