ABSTRACT
Many people despise mathematics, believing it to be nothing more than a confusing jumble of arcane formulas and mind-numbing computations. But in truth, mathematics is a beautiful, intricately structured tower of knowledge built up from a small collection of basic statements using the laws of logic. In logic and mathematics, language is used in a very precise way that does not always coincide with how words are used in everyday conversation. Two propositional forms A and B are logically equivalent when the truth tables for A and B have outputs that agree in every row. The names of the first three laws indicate the analogy between these logical equivalences and certain algebraic properties of real numbers. Certain propositional forms, called tautologies and contradictions, play a special role in logic and proofs. A propositional form A is called a tautology iff every row of the truth table for A has output true.
