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Propositional logic

  1. Nov 1, 2009 #1
    1. The problem statement, all variables and given/known data

    Either A or B (names changed) stole the exam answers. Formalize these and check if this is a correct deduction:
    1) If A didn't meet B for lunch, then B is guilty or A lives in the countryside
    2) If B isn't guilty, then A didn't meet B for lunch and the incident happened after dinner
    3) If it happened after dinner, then B is guilty, or A lives in the countryside
    4) It rained in the evening, and the teacher slept sound asleep
    5) And so, B is guilty

    3. The attempt at a solution

    "A met B for lunch" = P
    "B is guilty" = Q
    "A lives in the countryside" = R
    "it happened after dinner" = S
    "It rained in the evening" = T
    "the teacher slept sound asleep" = U

    Not actually sure but am I supposed to prove or disprove this? :

    [tex] P \rightarrow Q \vee R, \neg Q \rightarrow \neg P \wedge S, S \rightarrow Q \vee R, T \wedge U \models Q [/tex]
     
  2. jcsd
  3. Nov 1, 2009 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    Yep, that looks about right.

    Actually, T and U sound completely irrelevant, and you can probably reduce it to
    [tex]
    \{ P \rightarrow Q \vee R, \neg Q \rightarrow \neg P \wedge S, S \rightarrow Q \vee R \} \models Q
    [/tex]
     
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