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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Similar Questions
If $\sim p \lor q$ is false, then which of the following is correct?
Simplify $(p \vee q) \wedge (p \vee \sim q)$
The expression $((p \wedge q) \vee (p \vee \sim q)) \wedge (\sim p \wedge \sim q)$ is equivalent to
If the statement $p \vee \sim(q \wedge r)$ is false,then the truth values of $p, q$ and $r$ are respectively:
Consider the following three statements:
$P: 5$ is a prime number.
$Q: 7$ is a factor of $192$.
$R: \text{L.C.M. of } 5 \text{ and } 7 \text{ is } 35$.
Then,the truth value of which one of the following statements is true?
$P: 5$ is a prime number.
$Q: 7$ is a factor of $192$.
$R: \text{L.C.M. of } 5 \text{ and } 7 \text{ is } 35$.
Then,the truth value of which one of the following statements is true?
DifficultJEE MAIN 2019
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