If the statement $(p \vee \sim r) \rightarrow (q \wedge r)$ is false and the statement $q$ is true,then what is the truth value of statement $p$?

Which statement given below is a tautology?

The contrapositive of the statement 'If Jaipur is the capital of Rajasthan,then Jaipur is in India' is:

The statements $p, q$ and $r$ have truth values True, False and False respectively. The truth values of a logical statement $[\sim (p \land \sim q) \lor (q \lor \sim r)]$ and its dual are, respectively.....

Which of the following sentences are statements? Give reasons for your answer.
There are $35$ days in a month.

Which of the following statement$(s)$ is/are not true?
$I$) If $1$ is not a prime number, then $2$ is not a prime number.
$II$) $e$ is a vowel and $12 \times 3 = 36$.
$III$) It is not true that $14$ is a composite number and $3$ is an even number.
$IV$) $\sqrt{5}$ is an irrational number, but $3 + \sqrt{5}$ is a complex number.