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

If $$q$$ is false and $$p \wedge q \leftrightarrow r$$ is true, then ............ is a tautology.

Negation of contrapositive of statement pattern $$(p \vee \sim q) \rightarrow(p \wedge \sim q)$$ is