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Solution (c)

  • (c) “If I work, it is either sunny or partly sunny.” “I worked last Monday or I worked last Friday.” “It was not sunny on Tuesday.” “It was not partly sunny on Friday.”

  • There is no single relevant conclusion in this problem, its main difficulty is to to represent the premises so that one is able infer anything at all. One possible relevant conclusion is: “It was sunny or partly sunny last Monday or it was sunny last Friday.”.

  • Let the primitive statements be:

    • wm, ‘I worked last Monday’

    • wf , ‘I worked last Friday’

    • sm, ‘It was sunny last Monday’

    • st, ‘It was sunny last Tuesday’

    • sf , ‘It was sunny last Friday’

    • pm, ‘It was partly sunny last Monday’

    • pf , ‘It was partly sunny last Friday’

  • Then the premises are translated as: wm ∨ wf , wm → (sm ∨ pm), wf → (sf ∨ pf ), ¬st, and ¬pf .

  • And the conclusion: sf ∨ sm ∨ pm.

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