Graph G is connected if there is a path between every pair of vertices. We call G a tree if it is connected and does not contain a cycle.

Theorem: Let T be a tree on n vertices. Then T has n - 1 edges.

Lemma: Let G be a connected graph, and let e be an edge in G that is not contained in any cycle. Then, the graph obtained from G bt deleting e contains precisely two conponents.

Prove the theorem by using mathermatical induction and make use of the lemma which you can assume it is correct and do not have to prove.