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Thread: Negation of a sentence

  1. #1
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    Negation of a sentence

    I need to write the negation for each of the following. I've written out what I think it should be, but was hoping someone could check. I want to be sure I understand this.

    $\displaystyle \forall x \in Z, x < 0$

    Negation: $\displaystyle \exists x \in Z, x \not< 0$

    $\displaystyle \exists x \in Z, x = x + 1$

    Negation: $\displaystyle \forall x \in Z, x \neq x + 1$

    $\displaystyle \exists x \in N, x < 10$

    Negation: $\displaystyle \forall x \in N, x \not< 10$

    $\displaystyle \forall x \in N, x + x = 2x$

    Negation: $\displaystyle \exists x \in N, x + x \neq 2x$

    $\displaystyle \exists x \in Z, \forall y \in Z, x > y$

    Negation: $\displaystyle \forall x \in Z, \exists y \in Z, x \not> y$

    $\displaystyle \forall x \in Z, \exists y \in Z, x = y$

    Negation: $\displaystyle \exists x \in Z, \forall y \in Z, x \neq y$

    $\displaystyle \forall x \in Z, \exists y \in Z, x + y = 0$

    Negation: $\displaystyle \exists x \in Z, \forall y \in Z, x + y \neq 0$

    Would it be more proper to use the $\displaystyle \neg$ symbol, or are these okay?
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  2. #2
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    those all look good to me, and I don't use that symbol but then again I am not really dealing with logic tables too much
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  3. #3
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    Thanks
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