The conditional statement $(p \wedge q) \implies p$ is:

Let $S$ be a non-empty subset of $R$. Consider the statement $p : x \in S$ is a rational number such that $x > 0$. Which of the following is the negation of $p$?

Let $p$ and $q$ stand for the statements "$2 \times 4 = 8$" and "$4$ divides $7$" respectively. Then the truth values of the following biconditional statements are:
$(i)$ $p \leftrightarrow q$
$(ii)$ $\sim p \leftrightarrow q$
$(iii)$ $\sim q \leftrightarrow p$
$(iv)$ $\sim p \leftrightarrow \sim q$

Let $\Delta \in \{\wedge, \vee, \Rightarrow, \Leftrightarrow\}$ be such that $(p \wedge q) \Delta ((p \vee q) \Rightarrow q)$ is a tautology. Then $\Delta$ is equal to

For the given statement,identify the necessary and sufficient conditions.
$t:$ If you drive over $80 \, km/h$,then you will get a fine.

The statement $(p \wedge (p$ $\rightarrow q) \wedge (q$ $\rightarrow r))$ $\rightarrow r$ is :