Write the negation of the following statement:
$q:$ There exists a rational number $x$ such that $x^{2} = 2$.
$q:$ There exists a rational number $x$ such that $x^{2} = 2$.
(N/A) The negation of $q$ is denoted by $\sim q$,which means "it is false that $q$".
$\sim q:$ There does not exist a rational number $x$ such that $x^{2} = 2$.
This statement can also be expressed as:
$\sim q:$ For all rational numbers $x, x^{2} \neq 2$.
$\sim q:$ There does not exist a rational number $x$ such that $x^{2} = 2$.
This statement can also be expressed as:
$\sim q:$ For all rational numbers $x, x^{2} \neq 2$.
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