The main formulation rules for propositional expressions are Every elementary proposition is a propositional expression. The negation of a propositional expression yields a new propositional expression. Every combination of two propositional expressions by means of a logical connective is also a propositional expression. Rules of Precedence To keep the number of parentheses to a minimum, rules of precedence can be introduced to guarantee a desired meaning for a compound proposition. The order of evaluation is Evaluating Compound Propositions Truth tables can be used to calculate the truth values of the compound parts.
Examples Find the truth table for the expression .
A tautology is a logical expression that is always true regardless of the truth value of its components. Contradiction A contradiction is an expression which is false for all possible truth values of its components. If P is a tautology, then is a contradiction and vice versa. Examples Construct the truth table for . Construct a truth table for .