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Math Help - Negations Project

  1. #1
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    Negations Project

    What are the negations of the following statements?

    There does not exist 0 such that for all x, x+0=x

    The newspaper article was neither accurate nor entertaining.


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  2. #2
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    The first statement, in symbols is
     \not\exists 0 \forall x  x+0=x
    Which is equivalent to
     \forall y \forall x  x+y \neq x
    Which we negate as,
     \exists 0 \forall x, x+0=x.

    For the second example, english is very misleading. An equivalent statement is,
    the newspaper article was not accurate and not entertaining.

    So, the negation (by Demoivre's Law), is:
    the newspaper article was either accurate or entertaining.
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