Which of the following is equivalent to the Boolean expression $p \wedge \sim q$?

The contrapositive of the statement $\sim p \vee (q \wedge \sim r)$ is

Write the following statement in the form of "if-then":
To get an $A^{+}$ in the class,it is necessary that you do all the exercises of the book.

If the truth value of the compound statement $[(p \lor q) \land (q \to r) \land (\sim r)] \to (p \land q)$ is $False$, then the truth values of $p \to q$ and $q \to p$ are respectively......

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

The entries in the last column of the truth table for $\sim(p \wedge q)$ are