Question: Prove the following implications regarding free trees. (a) If an undirected graph is connected and has no simple cycles, THEN the graph has |V|

Prove the following implications regarding free trees.

(a) If an undirected graph is connected and has no simple cycles, THEN the graph has |V| − 1 edges.

(b) If an undirected graph has |V| − 1 edges and no cycles, THEN the graph is connected.

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