Let X = {2, 3, 6, 12, 24}. Define a partial order on X by x <= y if x divides…
1996
Let X = {2, 3, 6, 12, 24}. Define a partial order on X by x <= y if x divides y. The number of edges in the Hasse diagram of (X, <=) is
- A.
3
- B.
4
- C.
9
- D.
None of the above
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Correct answer: B
In a Hasse diagram, we draw only cover relations and omit edges implied by transitivity.
For divisibility on X = {2, 3, 6, 12, 24}, the cover relations are 2 < 6, 3 < 6, 6 < 12, and 12 < 24. Relations such as 2 < 12 or 6 < 24 are not edges because there is an intermediate element.
Thus the Hasse diagram has 4 edges, so option 2 is correct.