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

The negation of the statement "If $5 < 7$ and $7 > 2$,then $5 > 2$" is

The dual of the statement pattern $\sim p \wedge (q \vee t)$ is (where $t$ is a tautology and $c$ is a contradiction).

The dual of the converse of the inverse of the logical statement $p \to (q \to r)$ is equivalent to...

If $p, q$ and $r$ are three propositions,then which of the following combination of truth values of $p, q$ and $r$ makes the logical expression $\{(p \vee q) \wedge ((\sim p) \vee r)\} \rightarrow ((\sim q) \vee r)$ false?

If $p :$ It is raining today.
$q :$ $I$ go to school.
$r :$ $I$ will meet my friends.
$s :$ $I$ will go to watch a movie.
Then write the statement: 'If it does not rain today or $I$ do not go to school,then $I$ will meet my friends and go to watch a movie' in symbolic form.