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In this lecture, we delve into the fundamentals of mathematical proofs, beginning with an understanding of essential terminologies such as theorems and axioms. We will analyze the structure of proofs, focusing on universal quantifiers and logical steps like universal instantiation (UI) and universal generalization (UG). The discussion will then shift to various proof methods, including direct proofs, counterexample approaches, and proof by contradiction, with practical examples. Lastly, we...