For any two statements $p$ and $q,$ the negation of the expression $p \vee ( \sim p \wedge q)$ is

Check the validity of the statement given below by the method specified against it.
$q:$ If $n$ is a real number with $n > 3$,then $n^{2} > 9$ (by contradiction method).

Write the negation of the following statement:
$p:$ For every positive real number $x,$ the number $x-1$ is also positive.

For each of the following compound statements,first identify the connecting words and then break it into component statements.
$x=2$ and $x=3$ are the roots of the equation $3x^{2} - x - 10 = 0$.

The negation of the statement "$12$ is a multiple of $3$ and $12$ is a multiple of $4$" is:

Let,$p$: Ramesh listens to music.
$q$: Ramesh is out of his village.
$r$: It is Sunday.
$s$: It is Saturday.
Then the statement "Ramesh listens to music only if he is in his village and it is Sunday or Saturday" can be expressed as: