The Boolean expression $(p \wedge \sim q) \Rightarrow (q \vee \sim p)$ is equivalent to:

The correct logical equivalences from the following are:
$(I)$ $p \to (q \to r) \equiv (p \land q) \to r$
$(II)$ $(p \to q) \to r \equiv p \to (q \lor r)$
$(III)$ $(p \to q) \to r \equiv (p \to r) \land (\sim q \to r)$
$(IV)$ $p \to (q \to r) \equiv q \to (p \to r)$

Write the contrapositive and converse of the following statement:
If two lines are parallel,then they do not intersect in the same plane.

The negation of the statement "If an integer is greater than $4$ and less than $5$, then it is a multiple of $3$" is:

If $p$: It is raining and $q$: It is pleasant,then the symbolic form of "It is neither raining nor pleasant" is

If the Boolean expression $(p \wedge q) \circledast (p \otimes q)$ is a tautology,then $\circledast$ and $\otimes$ are respectively given by