Proofs: Rules and Applications

This lecture covers various rules of inference in propositional logic, including disjunctive syllogism, modus ponens, and fallacies like affirming the conclusion. It also explores quantified statements, such as universal instantiation and existential generalization, and their applications in constructing valid arguments. The instructor demonstrates how to prove theorems using direct and indirect methods, like proof by contraposition and contradiction, and discusses the importance of lemmas in mathematical proofs.