$\sim p \wedge q$ is logically equivalent to

Let $*, \square \in \{\wedge, \vee\}$ be such that the Boolean expression $(p * \sim q) \Rightarrow (p \square q)$ is a tautology. Then :

Given the statement: "If a quadrilateral is a parallelogram,then its diagonals bisect each other."
Identify the following statements as the contrapositive or converse of the given statement:
$(i)$ If the diagonals of a quadrilateral do not bisect each other,then the quadrilateral is not a parallelogram.
$(ii)$ If the diagonals of a quadrilateral bisect each other,then it is a parallelogram.

If the statement $p \leftrightarrow (q \rightarrow p)$ is false,then the true statement/statement pattern is

The dual of the converse of the inverse of the logical statement $p \to (q \to r)$ is equivalent to...

For each of the following statements,determine whether an inclusive "Or" or exclusive "Or" is used. Give reasons for your answer.
The school is closed if it is a holiday or a Sunday.