Propositional Logic and Truth Tables

Flashcards covering key definitions and truth table rules for propositional logic, including concepts like negation, conjunction, disjunction, implication, equivalence, XOR, tautology, contradiction, and contingent propositions.

For negation (¬p), if p is True, then ¬p is , and if p is False, then ¬p is .

False, True

In conjunction (p ∧ q), the result is True only if both p and q are _.

True

In disjunction (p ∨ q), the result is False only if both p and q are _.

False

In implication (p ⇒ q), the result is False only when p is _ and q is _.

True, False

In equivalence (p ⇔ q), the result is True when p and q have the _ truth value.

same

The "Exclusive OR" (XOR), defined as (p ∨ q) ∧ ¬(p ∧ q), means the compound proposition is true when p and q have _ truth values.

different

A compound proposition that is true under all possible assignments of truth values to its prime propositions is called a _ or a valid proposition.

tautology

A compound proposition which is false under all possible assignments of truth values to its prime propositions is called a _ or an inconsistent proposition.

contradiction

A compound proposition which is neither a tautology nor a contradiction is called a _ proposition.

contingent