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Claim1 If every vertex in a tree has odd degree, then the tree has an odd number of edges. Claim2 If every vertex in a

Claim1 If every vertex in a tree has odd degree, then the tree has an odd number of edges.

Claim2 If every vertex in a graph has odd degree, then the graph has an odd number of edges.

1. Describe a counterexample to Claim 1. 2. Prove Claim 1 by a direct method. 3. Demonstrate that Claim 2 is false by counterexample.

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