Page 2 of 2 FirstFirst 12
Results 16 to 21 of 21

Math Help - Logical statements

  1. #16
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    So you've got

    1. p\to q
    2. \neg p\to x
    3. y\to z
    4. a\to \neg x
    5. \neg y\to \neg q.

    You're asked to prove or disprove z\to a.

    Since all of your assumptions are implications, the only inference rules you need are modus ponens and modus tollens. In this case, you'd have to assume z, and try to show a. For modus ponens, you'd need to start somewhere with a z on the LHS of an implication. For modus tollens, you'd need to start somewhere with a \neg z on the RHS of an implication. That does not occur anywhere in your assumptions. Therefore, I deduce that you're not going to be able to prove z\to a. But how do you disprove it? You have to be able to assign truth values to all of the propositions such that all your assumptions are true, and yet z\to a is false. In order for z\to a to be false, z=\text{TRUE} and a=\text{FALSE}. So now see if you can assign the rest of the truth values of your propositions such that all the assumptions are satisfied. Make sense?
    Follow Math Help Forum on Facebook and Google+

  2. #17
    Senior Member
    Joined
    Apr 2009
    Posts
    306
    Ahhh yes thank you very much!!! I get it all now, excellent explanation!
    Follow Math Help Forum on Facebook and Google+

  3. #18
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    You're welcome. Have a good one!
    Follow Math Help Forum on Facebook and Google+

  4. #19
    Newbie
    Joined
    Aug 2010
    Posts
    1
    Quote Originally Posted by Plato View Post
    The bit above in red is incorrect.
    It should be: \text{“A only if B”} \equiv \left( {A \to B} \right).

    Reason: It says that A is true only if B is also true.
    The only condition we cannot allow is true implies false.
    Thanks for the help guys!

    Ackbeet, thanks for that pickup, that was a stupid mistake by me - however I was under the impression that "A if B" means B implies A, however "A only if B" means A implies B?

    _________________________________
    watch free movies online
    Follow Math Help Forum on Facebook and Google+

  5. #20
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Ackbeet, thanks for that pickup, that was a stupid mistake by me - however I was under the impression that "A if B" means B implies A, however "A only if B" means A implies B?
    See posts 8 - 10.
    Follow Math Help Forum on Facebook and Google+

  6. #21
    Senior Member
    Joined
    Apr 2009
    Posts
    306
    Um why did that person post exactly the same thing as I did on page 1? lol...
    Follow Math Help Forum on Facebook and Google+

Page 2 of 2 FirstFirst 12

Similar Math Help Forum Discussions

  1. Replies: 7
    Last Post: November 27th 2011, 11:39 AM
  2. [SOLVED] Confused about logical equivalence of some statements
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: July 13th 2011, 04:44 AM
  3. Replies: 1
    Last Post: July 8th 2011, 05:21 AM
  4. Prove/disprove using logical using logical arguments
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: February 24th 2010, 06:29 AM
  5. Replies: 3
    Last Post: January 21st 2010, 07:45 AM

Search Tags


/mathhelpforum @mathhelpforum