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Proofs: Logic, Mathematics & Algorithms
This lecture covers the concepts of proof, axiom, and theorem, different types of proofs (direct, contraposition, contradiction, by cases), fallacies in proofs, and practical applications of proofs in computer science. It also explains terminology, informal proofs, lemmas, corollaries, and conjectures. Various proof techniques such as direct proofs, proof by contraposition, proof by contradiction, exhaustive proof, proof by cases, and existence proofs are discussed with examples. The lecture also touches on uniqueness proofs, counterexamples, proofs of equivalence, and mistakes in proofs.