If every vertex in a simple undirected graph has non-zero degree, then the graph is connected.

(a) Prove that this claim is false by giving a counterexample.

(b) Since the claim is false, there must be a logical mistake in the following bogus proof. Pinpoint the first logical mistake (unjustified step) in the proof and explain why it is unjustified.

False Claim: If every vertex in a simple undirected graph has non-zero degree, then the graph is connected. (a) Prove that this claim is false by giving a counterexample (b) Since the claim is false, there must be a logical mistake in the following bogus proof. Pinpoint the first logical mistake (unjustified step) in the proof and explain why it is unjustified Bogus proof by induction: Let P(n) be the proposition that if every vertex in an n-vertex graph has non-zero degree, then the graph is connected Base Cases: (n