4: Disjunctive Syllogism

Disjunctive Syllogism

Key Terms

Modus Ponens
Modus Tollens
Disjunctive Syllogism

  • Presents alternatives
  • Similar Form

Disjunctive Syllogism

Premise(s): Either P or Q
Premise(s): Not P
Conclusion: Therefore, Q

  • If you replace P and Q with any sentence, this results in a valid argument
  • The first premise presents alternatives
  • The second premise denies one alternative
  • The conclusion affirms the remaining opinion


  • Either I left my wallet at home or I have lost it.
  • It’s not at home.
  • So I have lost it.


  • Either it is cloudy or it is sunny.
  • It is not cloudy.
  • Therefore it is sunny


  • Valid structure does not always lead to a sound argument
  • Perhaps my wallet was stolen
  • Perhaps it is not cloudy or sunny because it is night.
  • Disjunctive Syllogism speaks only to the format of the statement, not if it is true.