Results 1 to 3 of 3

Math Help - Quantifer Negation Help

  1. #1
    Junior Member
    Joined
    Feb 2008
    Posts
    64

    Quantifer Negation Help

    I have been reading on how to write the negation of quantifiers for a couple hours but am still confused as to how to give the answer:

    Give the Negation of the following:
    1. \forall z \in \mathbb{C}, \exists w \in \mathbb{C} : w^2 = z

    2. \forall x \in \mathbb{R}, (x<-2 \rightarrow x^2 >4)

    My Answer's (If correct)

    1. \exists z \in \mathbb{C}, \forall w \in \mathbb{C} : \neg (w^2 = z)

    2. \exists x \in \mathbb{R}, \neg (x<-2 \rightarrow x^2 >4)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Shanks's Avatar
    Joined
    Nov 2009
    From
    BeiJing
    Posts
    374
    Yeah, you are correct.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,616
    Thanks
    1579
    Awards
    1
    Quote Originally Posted by Stylis10 View Post
    I have been reading on how to write the negation of quantifiers for a couple hours but am still confused as to how to give the answer:

    Give the Negation of the following:
    1. \forall z \in \mathbb{C}, \exists w \in \mathbb{C} : w^2 = z

    2. \forall x \in \mathbb{R}, (x<-2 \rightarrow x^2 >4)

    My Answer's (If correct)

    1. \exists z \in \mathbb{C}, \forall w \in \mathbb{C} : \neg (w^2 = z)

    2. \exists x \in \mathbb{R}, \neg (x<-2 \rightarrow x^2 >4)
    I would expect these answers.
    1. \exists z \in \mathbb{C}, \forall w \in \mathbb{C} : w^2 \ne z)

    2. \exists x \in \mathbb{R}, (x<-2 ~\&~ x^2 \le4)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Negation
    Posted in the Discrete Math Forum
    Replies: 11
    Last Post: October 20th 2010, 12:10 PM
  2. Negation of x in A or B
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: October 13th 2010, 08:13 AM
  3. Negation help (2)
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: April 15th 2010, 07:49 AM
  4. Negation help
    Posted in the Discrete Math Forum
    Replies: 14
    Last Post: April 13th 2010, 09:20 AM
  5. The Negation
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: October 22nd 2009, 12:55 PM

Search Tags


/mathhelpforum @mathhelpforum