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Anonymous Posted 13 years ago
Grammar

propositional logic

sally is taking a taxi and, if it is raining, so is pat.

P: Sally is taking a taxi
Q: It is raining
R: Pat is taking a taxi

(P ^ ( --> Q ^ R))

I am unsure of the translation, any advice would be great!

( the sentence above, needed to be translated into propositional logic, i have shown the translation key, and represented the variables using : P Q R )
  

Top answer

Anonymous (P ^ ( --> Q ^ R)) This doesn't make sense. If it were mathematics, it would be like (6 + (= 5+3)), which is just as nonsensical. Your parentheses are misplaced, or the --> is misplaced, or something, who knows what.

— CalifJim

  • Anonymous (P ^ ( --> Q ^ R)) This doesn't make sense.
  • If it were mathematics, it would be like (6 + (= 5+3)), which is just as nonsensical.
  • Your parentheses are misplaced, or the --> is misplaced, or something, who knows what.
  • ^ is "and" --> is "if ...
  • " CJ
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6 Answers
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Anonymous(P ^ ( --> Q ^ R))
This doesn't make sense. If it were mathematics, it would be like (6 + (= 5+3)), which is just as nonsensical.

Your parentheses are misplaced, or the --> is misplaced, or something, who knows what.

^ is "and"
--> is "if ... then ..."

CJ
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That looks like Q --> (P and R), but it's been a while.

H.
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I think that would be "If it is raining then sally is taking a taxi and Pat is taking a taxi". That is true, but it does not tell us that Sally is taking a taxi if i is not raining

What we need is"Sally is taking a taxi and, if it is raining, Pat is taking a taxi"
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fivejedjonWhat we need is"Sally is taking a taxi and, if it is raining, Pat is taking a taxi"
Oh. I misread the OP's sentence, sorry. I didn't see the "and" before "if".

P and (Q --> R)

H.
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Henry74P and (Q --> R)
That seems OK to me, though I am very far from an expert here.
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Henry74P and (Q --> R)
Looks good to me, too. Also, using the OP's symbols,

P ^ (Q --> R)

[ PEE and if CUE then AR. ]

CJ
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