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

The statement $(p$ $\rightarrow (q$ $\rightarrow p))$ $\rightarrow (p$ $\rightarrow (p \vee q))$ is

For the given statement,identify the necessary and sufficient conditions.
$t:$ If you drive over $80 \, km/h$,then you will get a fine.

If the truth value of the compound statement $[(p \lor q) \land (q \to r) \land (\sim r)] \to (p \land q)$ is $False$, then the truth values of $p \to q$ and $q \to p$ are respectively...

The conditional $(p \wedge q) \Rightarrow p$ is :-

Consider the following statements.
$p: \text{If } 3^4 > 4^3, \text{then } 3^3 > 4^1$
$q: \text{The roots of the equation } x^2 - 2x + 2 = 0 \text{ are real if and only if Mumbai is in Maharashtra.}$
$r: \text{Statement } p \text{ is true or statement } q \text{ is false.}$
Which of the following has truth value $T$ (true)?