Final answer:
To draw the Hasse diagram for divisibility on the set {2,3,6,12,24,36,48,72}, start with the lowest element and draw arrows from one element to another if the first element divides the second. Repeat this process until all elements are connected.
Step-by-step explanation:
To draw the Hasse diagram for divisibility on the set {2,3,6,12,24,36,48,72}, we need to represent the elements of the set as nodes and draw an arrow between nodes A and B if A divides B. In this case, node A will be placed higher than node B. Starting with the lowest element, 2, we find that it divides 6 and 12, so we draw arrows from 2 to 6 and 12. Next, both 3 and 6 divide 12, so we draw arrows from 3 and 6 to 12. Continuing this process, we find that 2, 3, 6, and 12 all divide 24, so we draw arrows from them to 24. We repeat this process until all elements are connected. The Hasse diagram for this set is shown below:
2
|
3, 6
|
12, 24
|
36, 48
|
72