Prove that if an edge is removed from a tree the resulting g

Prove that if an edge is removed from a tree, the resulting graph is not a tree.

Solution

Consider a Graph T which is a tree. The tree has n vertices and n-1 edges and it is a connected graph that means there is no loop in the graph. When you remove one of the edge from the tree. The resulting graph is not connected and hence it is not a tree.