Drawing a Hasse Diagram
1,316
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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Karim B
Updated on February 19, 2020Comments
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Karim B over 3 years
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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Karim B over 8 yearsSo there isn't a greatest element and the least upper bound of {2} is 2?
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hmakholm left over Monica over 8 years@KarimB: Correct. In general, a one-element set always has the element itself as least upper bound as well as greatest lower bound.
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Karim B over 8 yearsThank you so much for clearing that up!