A → B

 A

 B

valid

Modus Ponens

A → B

¬B

¬A

valid

Modus Tollens

A → B

 B → C

 A → C

valid

Hypothetical Syllogism

A

!A → B

 B → C

 C

valid

Chain Argument

All Ps are Qs

 j is a P

 j is a Q

Predicate Instantiation

All Ps are Qs

 All Qs are Rs

All Ps are Rs

valid

Universal Syllogism

A ∨ B

 ¬ A

 B

valid

Disjunctive Syllogism

A → B

 B

A

invalid

Affirming the Consequent

A → B

¬ A

¬B

invalid

Denying the Antecedent