Write the negation of the following statement:
$q:$ All cats scratch.

Write the negation of the following statement:
Chennai is the capital of Tamil Nadu.

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

If the truth value of the Boolean expression $((p \vee q) \wedge (q$ $\rightarrow r) \wedge (\sim r))$ $\rightarrow (p \wedge q)$ is false,then the truth values of the statements $p, q, r$ respectively can be:

Let $S$ be a non-empty subset of $R$. Consider the statement $p : x \in S$ is a rational number such that $x > 0$. Which of the following is the negation of $p$?

The negation of the statement "All continuous functions are differentiable" is: