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.
Thanks for all the help!
The first statement, in symbols is
$\displaystyle \not\exists 0 \forall x$ $\displaystyle x+0=x$
Which is equivalent to
$\displaystyle \forall y \forall x$ $\displaystyle x+y \neq x$
Which we negate as,
$\displaystyle \exists 0 \forall x, $ $\displaystyle x+0=x$.
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.