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It is important to understand that the occurrence of a common form depends upon the relationship between its terms, not upon the names given to those terms.

For example, both of these arguments are Modus Ponens:

p→q

p

∴q

¬q→p

¬q

∴p

It is also important to understand that it doesn't matter which premise is listed first or which premise is listed second.

For example, both of these arguments are Modus Ponens:

p

p→q

∴q

¬q

¬q→p

∴p

VALID FORMS | INVALID FORMS |
---|---|

Modus Ponensp→q p ∴q One premise is an if...then statement, the other premise affirms the antecedent, and the conclusion affirms the consequent. | Fallacy of the Converse (Affirming the Consequent)
p→q q ∴p One premise is an if...then statement, the other premise affirms the consequent, and the conclusion affirms the antecedent. |

Modus Tollensp→q ¬q ∴¬p One premise is an if...then statement, the other premise denies the consequent, and the conclusion denies the antecedent. | Fallacy of the Inverse (Denying the Antecedent)
p→q ¬p ∴¬q One premise is an if...then statement, the other premise denies the antecedent, and the conclusion denies the consequent. |

Hypothetical Syllogismp→q q→r ∴p→r One premise is an if...then statement, another premise is an if...then statement whose antecedent matches the consequent of the other premise, and the conclusion results from this chain of reasoning. | Misuse of Hypothetical Syllogismsp→q p→r ∴q→r p→q r→q ∴p→r An incorrect attempt at Hypothetical Syllogism, in which two conditional premises agree in the antecedent, or agree in the consequent. |

Disjunctive Syllogismsp∨q ¬q ∴p p∨q ¬p ∴q One premise is an "or" statement, the other premise denies part of the "or" statement, and the conclusion affirms the other part. | Disjunctive Fallacies (Affirming a Disjunct)p∨q q ∴¬p p∨q p ∴¬q One premise is an "or" statement, the other premise affirms part of the "or" statement, and the conclusion denies the other part. |

VALID FORM |
---|

Disjunction Introductionp ∴p ∨ q |

Conjunction Eliminationp∧q ∴p |

Conjunction Introductionp q ∴p∧q |