Question

Which among the following is false
$\left(i\right)$ If $P$ is a statement, then $\sim P$ is also a statement
$\left(ii\right)$ Negation of $P$: ''$x$ is a positive number" is, ''$x$ is a negative number"
$\left(iii\right)$ If $P$ is a statement, then $\sim (\sim P)$ is not a statement

• A. Only $\left(iii\right)$
• B. Only $\left(ii\right)$
• C. $\left(i\right)$ and $\left(ii\right)$
• D. $\left(ii\right)$ and $\left(iii\right)$

Answer 1

The correct option is D $\left(ii\right)$ and $\left(iii\right)$

If $P$ is a statement, then $P$ is either true or false, so definitely $\sim P$ is also a statement.
Similarly $\sim (\sim P)$ is also a statement and it will be $P$ itself.
Also negation of ''$x$ is a positive number'' is ''$x$ is not a positive number''. (or) "$x$ is non negative number''
So, $\left(ii\right)$ and $\left(iii\right)$ are false statements.