If the statement $$\mathrm{p} \leftrightarrow(\mathrm{q} \rightarrow \mathrm{p})$$ is false, then true statement/statement pattern is

The statement $$[\mathrm{p} \wedge(\mathrm{q} \vee \mathrm{r})] \vee[\sim \mathrm{r} \wedge \sim \mathrm{q} \wedge \mathrm{p}]$$ is equivalent to

The negation of the statement

"The number is an odd number if and only if it is divisible by 3."

The statement $$[(p \rightarrow q) \wedge \sim q] \rightarrow r$$ is tautology, when $$r$$ is equivalent to