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

If $(p \wedge \sim r) \Rightarrow (q \vee r)$ is false and $q$ and $r$ are both false,then $p$ is

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.

Write the following statement in the form "if $p$,then $q$":
$p$: It is necessary to have a password to log on to the server.

Which of the following logical equivalences is always true?

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