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I Logically equivalent

  1. May 2, 2016 #1
    From the text it says (P -> Q) or (P -> R) is equivalent to P -> (Q or R)

    I tried to see if this is true so I tried
    [tex] (P \to Q) \lor (P \to R) \\
    (P \lor \neg Q) \lor (P \lor \neg R) \\
    P \lor \neg Q \lor \neg R \\
    P \lor \neg(Q \land R) \\
    P \to (Q \land R) [/tex]
    and
    [tex] P \to (Q \lor R) \\
    P \lor \neg(Q \lor R ) \\
    P \lor (\neg Q \land \neg R) \\
    (P \lor \neg Q) \land (P \lor \neg R) \\
    (P \to Q) \land (P \to R) [/tex]

    From what I've done its seems like they're not equivalent ?!?!?
     
  2. jcsd
  3. May 2, 2016 #2

    andrewkirk

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    The second line does not follow from the first.

    I think what you meant to write for the second line was
    $$(\neg P\vee Q)\vee (\neg P\vee R)$$
    which is not the same thing.
     
  4. May 2, 2016 #3

    AHHHH thank you!
     
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