Exercise · ZW-HASSE-DIAGRAM-001 · ★☆☆ Basic
In the Hasse diagram of the divisors of \(12\) under divisibility, how many edges are there?
Choose one option.
Show answer
- B. 7
Explanation
The covering pairs are \(1\!-\!2,\ 1\!-\!3,\ 2\!-\!4,\ 2\!-\!6,\ 3\!-\!6,\ 4\!-\!12,\ 6\!-\!12\): seven 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
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- ZW-HASSE-DIAGRAM-006 How many edges does the Hasse diagram of the divisors of 30 under divisibility have?
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