Finite Math Logic - Vocabulary Flashcards

Vocabulary flashcards covering logic symbols, statement forms, valid/invalid patterns, De Morgan’s laws, and truth-table implications.

∧ (AND)

Conjunction; both P and Q must be true for P ∧ Q to be true.

∨ (OR)

Disjunction; at least one of P or Q is true for P ∨ Q to be true.

→ (IF…THEN)

Implication; P → Q is false only if P is true and Q is false; true in all other cases.

↔ (IF AND ONLY IF)

Biconditional; P ↔ Q is true when P and Q have the same truth value (both true or both false).

¬ (NOT)

Negation; inverts the truth value of a proposition.

Original Form

The conditional form: If P, then Q.

Converse Form

The converse: If Q, then P.

Inverse Form

The inverse: If not P, then not Q.

Contrapositive Form

The contrapositive: If not Q, then not P.

Original and Contrapositive Equivalence

P → Q is logically equivalent to its contrapositive ¬Q → ¬P.

Modus Ponens

If P → Q and P, then Q.

Modus Tollens

If P → Q and ¬Q, then ¬P.

Affirming the Consequent (Invalid)

Invalid form: If P → Q and Q, then P.

Denying the Antecedent (Invalid)

Invalid form: If P → Q and ¬P, then ¬Q.

De Morgan’s Law 1

¬(P ∧ Q) = ¬P ∨ ¬Q (Negation distributes over ∧ to ∨).

De Morgan’s Law 2

¬(P ∨ Q) = ¬P ∧ ¬Q (Negation distributes over ∨ to ∧).

P ∧ Q Truth Condition

True only when both P and Q are true.

P ∨ Q Truth Condition

True if at least one of P or Q is true.

P → Q Truth Condition

False only when P is true and Q is false.

P ↔ Q Truth Condition

True when P and Q have the same truth value.