Lecture 3 - PHIL222: Truth Tables and Logical Propositions

Flashcards containing key concepts and definitions related to propositional logic and truth tables.

WFF (Well-formed formula)

A string of symbols that is formed according to the syntax rules of a formal language.

Semantics of PL

The study of how well-formed formulas (wffs) relate to truth and falsity in propositional logic.

Bivalence Assumption

The principle that each proposition is either true or false, but not both.

Truth Values

The values assigned to propositions that signify their truth or falsity, represented as T (True) and F (False).

Truth-functional Connectives

Connectives in propositional logic where the truth or falsity of compound propositions depends entirely on the truth or falsity of their components.

Negation

A logical operation that takes a proposition and turns it into a proposition that is true if the original proposition is false, and vice versa.

Conjunction (∧)

A logical operation that is true if both of its conjuncts are true; otherwise, it is false.

Disjunction (∨)

A logical operation that is true if at least one of its disjuncts is true; otherwise, it is false.

Conditional (→)

A logical operation that is false only when the antecedent is true and the consequent is false; otherwise, it is true.

Biconditional (↔)

A logical operation that is true when both propositions have the same truth value; otherwise, it is false.

Truth Table

A table used to determine the truth values of a compound proposition by enumerating all possible truth values of its components.

Complex Proposition

A proposition that is composed of one or more simple propositions connected by logical connectives.

Main Connective

The primary logical connective in a complex proposition that determines its overall truth value.

Matrix of the Truth Table

The column in a truth table that displays all possible truth values of the basic propositions.

Body of the Truth Table

The part of the truth table that shows the outcome of the compound formula based on the basic propositions.

Row of the Truth Table

A single case of truth values in the truth table, representing a combination of truth values for the basic propositions.