Exercise · ZW-HASSE-DIAGRAM-007 · ★★☆ Intermediate
How many edges does the Hasse diagram of \(\{1,2,4,8,16,32\}\) under divisibility have?
Choose one option.
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- A. 5
Explanation
It is a total order: the chain \(1-2-4-8-16-32\) has \(6\) vertices and \(5\) edges.
Review the concept: Hasse diagram
A Hasse diagram draws a partially ordered set \((S,\preceq)\) with one point per element and an edge only between consecutive elements, placing the smaller one lower.
\[a\ \text{covers}\ b\iff b\prec a\ \wedge\ \nexists\,c:\ b\prec c\prec a\]
More practice problems: hasse diagram
- ZW-HASSE-DIAGRAM-001 In the Hasse diagram of the divisors of 12 under divisibility, how many edges are there?
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- ZW-HASSE-DIAGRAM-003 In the divisors of 12 under divisibility, which pair is an edge of the Hasse diagram?
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- ZW-HASSE-DIAGRAM-005 Why does a Hasse diagram draw no loops and no edges that follow by transitivity?
- ZW-HASSE-DIAGRAM-006 How many edges does the Hasse diagram of the divisors of 30 under divisibility have?
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- ZW-HASSE-DIAGRAM-009 How many elements does the longest chain in the Hasse diagram of the divisors of 60 under divisibil…