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17 December, 14:35

Provided that Alice but not the Hatter is cross unless mad, the Hatter, but not Alice, is mad unless frowning." How do you symbolize this sentence logically?

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  1. 17 December, 16:49
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    Well, it is a little tricky, but here is what I got:

    (P ∨ R) ∧ ∼ (S ∨ U) → (U ∨ T) ∧ ∼ (R ∨ Q)

    Explanation:

    First the Symbols:

    P: Alice is mad.

    Q: Alice frowns.

    R: Alice is mad

    S: The hatter is cross

    T: The hatter frowns

    U: The Hatter is mad

    *It is arbitrary, though, you can choose other symbols.

    I think the difficult part is that the "but not the Hatter" means that the whole statement that applies to Alice is negated for the Hatter.
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