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If A then B
A
B
Modus Ponens, Valid
If A then B
Not B
Not A
Modus Tollens, Valid
If A then B
B
A
Affirming the Consequent, Invalid
If A then B
Not A
Not B
Denying the Antecedent, Invalid
If A then B
If B then C
If A then C
Hypothetical Syllogism, Valid
A or B
Not A
B
A or B
Not B
A
Disjunctive Syllogism, Valid
A or B
A
Not B
A or B
B
Not A
Affirming the Disjunctive, Invalid