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?

Question

Social Studies

Cooper Bean

16 May, 21:13

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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Answers (1)

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Hadassah Mcintyre · Answer 1

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.