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Solution (a)

  • (a) “If I eat spicy foods, then I have strange dreams.” “I have strange dreams if there is thunder while I sleep.” “I did not have strange dreams.”
  • The relevant conclusions are: “I did not eat spicy food” and “There is no thunder while I sleep”.
  • Let the primitive statements be:
    • s, ‘I eat spicy foods’
    • d, ‘I have strange dreams’
    • t, ‘There is thunder while I sleep’
  • Then the premises are translated as: s → d, t → d, and ¬d.
  • And the conclusions: ¬s, ¬t.
  • Steps        Reason
  1. s → d        premise
  2. ¬d             premise
  3. ¬s             Modus Tollens to Steps 1 and 2
  4. t → d        premise
  5. ¬t             Modus Tollens to Steps 4 and 2.

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