What is the difference between affirming the consequent and denying the antecedent?

Affirming the consequent and denying the antecedent are both logical fallacies that occur in hypothetical syllogisms, but the two fallacies have different forms.

Affirming the consequent takes the following form:

  • If P, then Q.
  • Q.
  • Therefore, P.
Affirming the consequent example
  • If it’s summer, then the temperature will be high.
  • The temperature is high.
  • Therefore, it is summer.

Denying the antecedent takes the following form:

  • If P, then Q.
  • Not P.
  • Therefore, not Q.
Denying the antecedent example
  • If I study hard, then I’ll pass the exam.
  • I didn’t study hard.
  • Therefore, I won’t pass the exam.