Which of the following is false?

If $(p \wedge \sim r) \rightarrow (\sim p \vee q)$ has truth value $F$,then the truth values of $p, q,$ and $r$ are respectively:

Negation of the statement: $\sqrt{5}$ is an integer or $5$ is irrational is

Write the following statement in the form of "if-then":
The banana trees will bloom if it stays warm for a month.

Which of the following statements 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.

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.