Let there be a tree with at least two vertices. One vertex has degree $k$ and the other has degree $l$. Prove that such tree has at least $k + l - 2$ leaves.
My logic is that from one vertex you can reach at least $k$ leaves and from the other vertex you can reach at least $l$ leaves. But how exactly would I prove that you have to subtract $2$? Is it because if you start from one of the given vertices and go through the second one, then one of the leaves will be a duplicate?