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

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

The dual of the statement $[p \vee (\sim q)] \wedge (\sim p)$ is

The negation of the compound statement $\sim p \vee (p \vee (\sim q))$ is

Using the words "necessary and sufficient",rewrite the statement "The integer $n$ is odd if and only if $n^{2}$ is odd". Also,check whether the statement is true.