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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
- s → d premise
- ¬d premise
- ¬s Modus Tollens to Steps 1 and 2
- t → d premise
- ¬t Modus Tollens to Steps 4 and 2.
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