Results 1 to 3 of 3

Math Help - [SOLVED] Propositional functions and quantifiers ...

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    1

    Unhappy [SOLVED] Propositional functions and quantifiers ...

    x
    Last edited by princessleia; October 22nd 2008 at 04:42 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    \left( {\exists x} \right)\left( {\forall z} \right)\left[ {F(A,x) \wedge M(S,x) \wedge \left[ {F(A,z) \wedge M(S,z) \Rightarrow \left( {x = z} \right)} \right]} \right]
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Oct 2008
    Posts
    39
    Quote Originally Posted by princessleia View Post
    Let F(x, y) be the propositional function "x is the father of y", and let M(x, y) be the propositional function "x is the mother of y". Using only these two propostional functions and quantifiers, express the statement "Al and Sue have exactly one child" symbolically.


    I don't even know where to start with this one! Any ideas?

    To express in quantifier notation that Al and Sue have exactly one child we write:


    \exists !y[ F( A,y) & M( S,y)] ,which means there is a unique child (y) ,lets say ,of whom Al and Sue are the father and mother respectively:


    Now that formula is equivalent to the following formula:


    \exists y[ F( A,y) & M( S,y)]& \forall y\forall z{[F( A,y) & M( S,Y)] & [ F( A,z) & M( S,z)]------> y=z}:


    The 2nd formula means that Sue and Al have a child and their child is the only one (expressed by the 2nd part of the formula: \forall y\forall z{[F( A,y) & M( S,Y)] & [ F( A,z) & M( S,z)]------> y=z}:


    NOW if my 2nd formula is equivalent to that given by Plato ,one should be able to prove that.


    I think it is a good exercise for you
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 11
    Last Post: November 15th 2009, 11:22 AM
  2. Replies: 1
    Last Post: August 26th 2009, 08:04 AM
  3. Replies: 7
    Last Post: August 12th 2009, 04:41 PM
  4. [SOLVED] Using quantifiers and the preposition
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: December 16th 2008, 07:32 PM
  5. Replies: 15
    Last Post: June 3rd 2008, 03:58 PM

Search Tags


/mathhelpforum @mathhelpforum