Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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]
    [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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted