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Proof by Inference

  1. Mar 22, 2013 #1
    1. The problem statement, all variables and given/known data
    Asked to either prove or make a counter example:

    p ----> q
    (q and r) ----> s
    r
    -------------------------------
    p------> s

    2. Relevant equations



    3. The attempt at a solution

    I am having trouble making the step to the law of syllogism I know I need to solve this. Can anyone help me with stepping this our using the rules of inference. I would greatly appreciate this thanks.
     
  2. jcsd
  3. Mar 23, 2013 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    Usually my first instinct when I need to prove an implication is to assume the precedent and prove the conclusion. I.e. in this case, try to prove

    [itex]p \implies q[/itex]
    [itex](q \wedge r) \implies s[/itex]
    [itex]r[/itex]
    [itex]p[/itex]
    -------------------------------
    [itex]s[/itex]

    I think (hope) the next step is more obvious when put like this.
     
  4. Mar 24, 2013 #3
    Thanks that, got the proof based on that info. :D
     
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