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# Check whether the two statements given are negation of each other or not. Give reason " $p: x+y=y+x$ is true for every real number $x\:\:and\:\:y$. $q:$ There exists real numbers $x\:\:and\:\:y$ for which $x+y=y+x$.

$\begin{array}{1 1} yes \\ no \end{array}$

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## 1 Answer

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The given statements are:
$p: x+y=y+x$ is true for every real number $x\:\:and\:\:y$.
$q:$ There exists real numbers $x\:\:and\:\:y$ for which $x+y=y+x$
Negation of $p$ is
$x+y=y+x$ is not true for every real number $x\:\:and\:\:y$
That is $x+y\neq y+x$ for every real number $x\:\:and\:\:y$
But this is not the statement $q$.
$\therefore$ Both the statements $p\:\:and\:\:q$ are not the negation of each other.
answered Jul 16, 2014

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