Assume you have a forest with k connected components. Prove that if you added $k$ edges, you would obtain a cycle.
I’m thinking these facts/theorems may be useful...
In a forest, each component is a tree so each tree of order $n$ must have $n-1$ edges.
If $F$ is a forest of order $n$ containing $k$ connected components, then $F$ contains $n-k$ degrees.
I’m just not sure how to prove that I am guaranteed to get a cycle by adding k edges.