Common Deductive Argument Forms

Valid Form		Invalid Cousin
Modus Ponens	If P, then Q. P. __________ Q.	Affirming the Consequent	If P, then Q. Q. __________ P.
Modus Tollens	If P, then Q. Not-Q. ___________ Not-P.	Denying the Antecedent	If P, then Q. Not-P. __________ Not-Q.
Disjunctive Syllogism	Either P or Q. Not-P. _____________ Q.	Dysfunctional Syllogism (Inclusive ‘or’)	Either P or Q. Q. ____________ Not-P.
Hypothetical Syllogism	If P, then Q. If Q, then R. _____________ If P, then R.	Illegitimate Syllogism	If P, then Q. If R, then Q. __________ If P, then R.
Dilemma	Either P or Q. If P, then R. If Q, then R. ___________ R.	False Dichotomy	Either P or Q (or S). If P, then R. If Q, then R. __________ R.
Contraposition	If P, then Q. ___________ If not-Q, then not-P.	Conversion	If P, then Q. __________ If Q, then P.
Simplification	P and Q. _______ P.	Conjunction	P. ________ P and Q.
Addition	P. _______ P or Q.	Subtraction	P or Q. ________ P.