Results 1 to 5 of 5

Math Help - Can someone check my logic (sentential logic)

  1. #1
    Junior Member
    Joined
    Nov 2009
    Posts
    38

    Can someone check my logic (sentential logic)

    D: Dan is Married
    G: George is Married
    F: Fred is Married

    At most one of them is married.

    I figured you have just have to take the negation of the cases where two or more people are married (three cases), and the case when all of them are married. So I did this:

    \neg\left[\left(\left(G\&\left(F\&D\right)\right)\vee(G\&D))  \vee((G\&F)\vee(F\&D))\right]
    Last edited by swtdelicaterose; July 12th 2010 at 04:37 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    That's one valid approach. The other valid approach would be to OR the admissible cases together:

    D\vee F\vee G\vee\neg(D\vee F\vee G).

    [EDIT]: See Plato's post below for a correction to this approach.

    I think you'll find this approach more scalable, if you throw more guys into the mix!

    Incidentally, because disjunction is associative, you probably don't need that many parentheses, unless your teacher is being a stickler about wff's.
    Last edited by Ackbeet; July 13th 2010 at 04:09 AM. Reason: Incorrect.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,607
    Thanks
    1574
    Awards
    1
    The following is a true statement if all three were married.
    D\vee F\vee G\vee\neg(D\vee F\vee G).

    We want at most one is married.
    (\neg D \wedge \neg F \wedge \neg G) \vee (D \wedge \neg F \wedge \neg G) \vee (\neg D \wedge F \wedge \neg G) \vee (\neg D \wedge \neg F \wedge G).
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jun 2009
    Posts
    12
    \neg ( ( D \wedge F ) \vee (D \wedge G) \vee (F \wedge G) )
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jun 2009
    Posts
    12
    remember

    (D \wedge F \wedge G) \to (D \wedge F)
    (D \wedge F \wedge G) \to (D \wedge G)
    (D \wedge F \wedge G) \to (F \wedge G)

    so you don't need to care of

    (D \wedge F \wedge G)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Sentential Derivation (logic) help please
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: July 30th 2010, 08:16 PM
  2. sentential logic derivations?
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: November 19th 2009, 03:27 PM
  3. Sentential Logic Problem
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: October 7th 2009, 06:00 AM
  4. Logic Check with Set proof
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: September 16th 2009, 01:43 AM
  5. Logic, please check my answer
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: November 3rd 2008, 10:47 AM

Search Tags


/mathhelpforum @mathhelpforum