Explain why the following proof does not work. (It has a huge bug.) Problem: Half-Clique. Does G have a clique of size at least n/2? Proof: To show Half-Clique is in NP, the certificate is a list of n/2 vertices. We can check the edges in polynomial time to ensure that the vertices in the list form a clique of the right size in G Reduction: We reduce from Full-Clique below. Full-Clique: Does
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