Truth Table Generator. This tool generates truth tables for propositional logic formulas. You can enter logical operators in several different formats. For example, the propositional formula p ∧ q → ¬r could be written as p /\ q -> ~r, as p and q => not r, or as p && q ->!r. The connectives ⊤ . Truth Tables, Tautologies, and Logical Equivalences. Mathematicians normally use a two-valued logic: Every statement is either True or getfreeonlinequotes.com is called the Law of the Excluded Middle.. A statement in sentential logic is built from simple statements using the logical connectives,,,, getfreeonlinequotes.com truth or falsity of a statement built with these connective depends on the truth or falsity of. The logic gate truth table or truth tables used for electronic logic gates circuits including the AND, NAND, OR, NOR and exclusive OR circuits.