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Solution (b)

  • (b) “I am dreaming or hallucinating.” “I am not dreaming.” “If I am hallucinating, I see elephants running down the road.”

  • The relevant conclusion is: “I see elephants running down the road.”.

  • Let the primitive statements be:

    • d, ‘I am dreaming’

    • h, ‘I am hallucinating’

    • e, ‘I see elephants running down the road’

  • Then the premises are translated as: d ∨ h, ¬d, and h → e.

  • And the conclusion: e.

  • Steps           Reason

  1. d ∨ h            premise

  2. ¬d                premise

  3. h                  rule of disjunctive syllogism to Steps 1 and 2

  4. h → e          premise

  5. e                 Modus Ponens to Steps 4 and 3


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