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(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:
d ∨ h premise
h rule of disjunctive syllogism to Steps 1 and 2
h → e premise
e Modus Ponens to Steps 4 and 3
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