If $(\sim p \wedge q) \rightarrow r$ is false,then the truth values of $p, q, r$ are respectively:

Identify the type of "Or" used in the following statement and check whether the statement is true or false:
To enter into a public library,children need an identity card from the school or a letter from the school authorities.

Let $p$ and $q$ be two statements. Then $\sim(p \wedge (p \Rightarrow \sim q))$ is equivalent to:

Which of the following statements is a tautology?

Find the component statements of the following and check whether they are true or not.
$24$ is a multiple of $2, 4$ and $8$.

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