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Rewrite the given statement about Sherlock Holmes and Moriarty using logical symbols and expressions.

Sherlock Holmes will neither play his violin nor ask Watson for the needle; nevertheless, neither he nor Watson will fail to be baffled by Moriarty.

User Courtland
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Final answer:

The logical expression of the given statement can be notated as \(\\eg P \land \\eg Q\) and \(\\eg(\\eg R)\), where P, Q, and R represent Holmes playing the violin, asking Watson for the needle, and both being baffled by Moriarty, respectively.

Step-by-step explanation:

The statement 'Sherlock Holmes will neither play his violin nor ask Watson for the needle; nevertheless, neither he nor Watson will fail to be baffled by Moriarty' can be translated into logical symbols and expressions as follows:

Let P represent 'Holmes plays his violin', Q represents 'Holmes asks Watson for the needle', and R represents 'Holmes and Watson are baffled by Moriarty'.

The statement can then be written as:

\(\\eg P \land \\eg Q\) and \(\\eg(\\eg R)\)

This expression states that both P and Q are not true, and R is also true, which matches the original English statement. Notationally, the neither-nor construction is represented by negations combined with a conjunction, and the negation of a negation represents the word 'fail to'.

User Golvellius
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