Write the negation of the following statement:
Every natural number is an integer.

Which of the following logical equivalences is true?

The Boolean expression $\sim (p \Rightarrow (\sim q))$ is equivalent to

$(S1) (p \Rightarrow q) \vee (p \wedge (\sim q))$ is a tautology. $(S2) ((\sim p) \Rightarrow (\sim q)) \wedge ((\sim p) \vee q)$ is a contradiction. Then

The contrapositive of $\sim q \to p$ is equivalent to

If $p: \text{A man is happy}$,$q: \text{A man is rich}$,then the symbolic form of '$\text{A man is neither happy nor rich}$' is