Dive into the foundational concepts of propositional logic, compound propositions, tautologies, and contradictions in this comprehensive university-level mathematics lecture for Ethiopian freshmen. Explore the fundamental principles of logical reasoning, learn to construct and analyze complex propositions, and understand the critical distinctions between always-true tautologies and always-false contradictions. Enhance your mathematical thinking and problem-solving skills through this essential introduction to formal logic, setting a strong foundation for advanced mathematical studies.