Foundations: Logic and Proofs - Propositional Logic

These flashcards cover fundamental concepts in propositional logic, including definitions and examples related to propositions, logical connectives, and implication.

Proposition

A declarative sentence that is either true or false.

Connectives

Logical operators that combine propositions, including negation, conjunction, disjunction, implication, and biconditional.

Negation (¬)

The logical operation that takes a proposition p and produces the statement 'not p'.

Conjunction (∧)

A logical connective that returns true if both propositions are true; denoted as p ∧ q.

Disjunction (∨)

A logical connective that returns true if at least one of the propositions is true; denoted as p ∨ q.

Implication (→)

A logical connective representing 'if p, then q', which is true unless p is true and q is false.

Biconditional (↔)

A logical connective denoting 'p if and only if q', which is true when both propositions are either true or false.

Truth Table

A table used to compute the truth values of various propositions based on the logical connectives applied.

Converse

The statement formed by reversing the hypothesis and conclusion of an implication, represented as q → p.

Contrapositive

The statement formed by negating both the hypothesis and the conclusion, represented as ¬q → ¬p.

Inverse

The statement formed by negating the hypothesis and conclusion of an implication, represented as ¬p → ¬q.

Compound Proposition

A proposition formed from two or more propositions using logical connectives.

Inclusive Or

A type of disjunction where the statement is true if at least one of the propositions is true; can be both.

Exclusive Or (Xor)

A type of disjunction where the statement is true if exactly one of the propositions is true, but not both.