Disjunctive Syllogism

Disjunctive syllogism, also known as Modus Tollendo Tollens is a rule of inference of Propositional logic that states that if P or Q is true and not P is true, then Q is true.

In standard rule form:

$\frac{P \or Q, \neg P}{\therefore Q}$

In sequent notation:

$P \or Q, \neg P \vdash Q$

It is the valid argument form: P or Q. Not P. Therefore, Q.

Natural Deduction Transformation Rules

Rules of inference

Modus Ponens | Modus Tollens | Disjunctive Syllogism | Hypothetical Syllogism | Conjunction Introduction | Conjunction Elimination | Disjunction Introduction | Disjunction Elimination | Bicondional Introduction | Biconditional Elimination | Constructive Dilemma | Destructive Dilemma | Absorption | Modus ponendo tollens

Rules of Transformation

Double Negation | Associative property | Commutative property | Distributive property | DeMorgan's Laws | Tautology | Exportation | Material Implication | Transposition