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
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.