Discrete Mathematics - Rules of Inference

Argument

sequence of statements that end with a conclusion.

Valid

conclusion that must follow the truth of the preceding statements

Premises

proceeding statements

Fallacies

incorrect reasoning

Rules of inference

simple argument forms

Law of detachment

tautology also known as Modus ponens mode that affirms

p

p → q

∴ q

Modus Ponens

(p ∧ (p → q)) → q

¬q

p → q

∴ ¬p

Modus tollens

(¬q ∧ (p → q))→¬p

p → q

q → r

∴ p → r

Hypothetical syllogism

((p → q) ∧ (q → r)) → (p → r)

p ∨ q

¬p

∴ q

Disjunctive syllogism

((p ∨ q)∧¬p) → q

p

∴ p ∨ q

Addition

p → (p ∨ q)

p ∧ q

∴ p

Simplification

(p ∧ q) → p

p

q

∴ p ∧ q

Conjunction

((p) ∧ (q)) → (p ∧ q)

p ∨ q

¬p ∨ r

∴ q ∨ r

Resolution

((p ∨ q) ∧ (¬p ∨ r)) → (q ∨ r)