Results 1 to 2 of 2

Math Help - Nest quantifiers and determining truth value

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    5

    Nest quantifiers and determining truth value

    I must be misunderstanding something...

    Here's the issue. I'm going to use A and E as my universal and existential quantifiers because I don't know how to type upside down A's and backwards E's.

    Q(x,y) is "x + y = x - y"; domain is all integers

    AxEyQ(x,y)

    For every integer x there is a integer y such that Q(x,y).

    My understanding is...this is true when, for every x there is a y for which Q(x,y) is true. Looking at x + y = x - y...if y=0, then x=x. So this whole thing should be true. Correct?

    BUT...my other understand is that, when there is an x such that Q(x,y) is false for every y, then the whole thing is false. Is this correct? So if you let x=0....then y=-y, which is always false. So then the whole thing is false.

    It can't be both! What am I not getting right?

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Jan 2010
    Posts
    5
    Oops...never mind...I'm dumb.

    For x+y=x-y, setting x=0 is not false for the case y=0. And there is no x such that Q(x,y) if false for every y. So the entire logic statement cannot be false.

    I think I got it. However, if I'm still stupid, please let me know! Thanks!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. quantifiers
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: August 2nd 2011, 03:10 AM
  2. Replies: 1
    Last Post: August 26th 2009, 09:04 AM
  3. Determining the Truth of Statements
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: October 31st 2008, 06:08 PM
  4. Quantifiers
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: June 7th 2008, 07:31 PM

Search Tags


/mathhelpforum @mathhelpforum