The Divisibility DAG
![](/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-spring-2015/structures/tp7-1/vertical-839e7a19a176/divi2.gif)
In the above DAG for the divisibility relation on \(\{1, \ldots, 12\}\), there is an upward path from \(a\) to \(b\) iff \(a\) divides \(b\). If \(24\) was added as a vertex, what is the minimum number of edges that must be added to the DAG to represent divisibility on \(\{1, \ldots, 12, 24\}\)?