Which of the following statements is a tautology?
$((\sim p) \vee q) \Rightarrow p$
$p \Rightarrow((\sim p ) \vee q )$
$((\sim p) \vee q) \Rightarrow q$
$q \Rightarrow((\sim p) \vee q)$
The statement $(\mathrm{p} \wedge(\mathrm{p} \rightarrow \mathrm{q}) \wedge(\mathrm{q} \rightarrow \mathrm{r})) \rightarrow \mathrm{r}$ is :
$\left( {p \wedge \sim q \wedge \sim r} \right) \vee \left( { \sim p \wedge q \wedge \sim r} \right) \vee \left( { \sim p \wedge \sim q \wedge r} \right)$ is equivalent to-
The statment $ \sim \left( {p \leftrightarrow \sim q} \right)$ is
Suppose $p, q, r$ are positive rational numbers such that $\sqrt{p}+\sqrt{q}+\sqrt{r}$ is also rational. Then
Which of the following statement is a tautology?