The negation of the statement $$((A \wedge(B \vee C)) \Rightarrow(A \vee B)) \Rightarrow A$$ is

Among the two statements

$$(\mathrm{S} 1):(p \Rightarrow q) \wedge(p \wedge(\sim q))$$ is a contradiction and

$$(\mathrm{S} 2):(p \wedge q) \vee((\sim p) \wedge q) \vee(p \wedge(\sim q)) \vee((\sim p) \wedge(\sim q))$$ is a tautology

The converse of $$((\sim p) \wedge q) \Rightarrow r$$ is

The statement $$\sim[p \vee(\sim(p \wedge q))]$$ is equivalent to :