Let the operations $*, \odot \in\{\wedge, \vee\}$. If $( p * q ) \odot( p \odot \sim q )$ is a tautology, then the ordered pair $(*, \odot)$ is.

Let $p, q, r$ denote arbitrary statements. Then the logically equivalent of the statement $p\Rightarrow (q\vee r)$ is

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

$\left(p^{\wedge} r\right) \Leftrightarrow\left(p^{\wedge}(\sim q)\right)$ is equivalent to $(\sim p)$ when $r$ is.

Negation of the conditional : “If it rains, I shall go to school” is

If $p, q, r$ are simple propositions with truth values $T, F, T$, then the truth value of $(\sim p \vee q)\; \wedge \sim r \Rightarrow p$ is