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2. Translate the proposition to symbolic form (including delimiters) using the indicated variable:     "Paula (P) and Quentin (Q) are going to the pub but Roger (R) won't go if Sandra (S) does."

Question

  1. Translate the proposition to symbolic form (including delimiters) using the indicated variable:     "Paula (P) and Quentin (Q) are going to the pub but Roger (R) won't go if Sandra (S) does."
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Solution

The proposition "Paula (P) and Quentin (Q) are going to the pub but Roger (R) won't go if Sandra (S) does." can be translated to symbolic form as follows:

(P ∧ Q) ∧ (¬S → R)

Here's the step by step translation:

  1. "Paula (P) and Quentin (Q) are going to the pub" translates to (P ∧ Q). The symbol ∧ represents the logical conjunction "and".

  2. "Roger (R) won't go if Sandra (S) does" translates to (¬S → R). The symbol ¬ represents the logical negation "not", and → represents the logical implication "if...then".

  3. The word "but" in the sentence can be considered as another "and", so the whole sentence translates to (P ∧ Q) ∧ (¬S → R).

This problem has been solved

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