Explore the mathematical framework of the Algebra of Boole as an alternative to Propositional Logic in this 35-minute video lecture. Learn how to replace truth tables and Boolean equivalences with a simplified algebraic approach using 0's and 1's. Discover the process of computing Boole polynumbers for ingredient clauses to verify statements. Examine specific examples, including the non-obvious Distributive Law and Transitivity of Implication (Hypothetical Syllogism). Gain insights into this powerful technique for systematizing reasoning and modeling logical connectives such as AND, OR, NOT, IMPLIES, and EQUIVALENT.