The statement $[(p \wedge q)$ $\rightarrow p]$ $\rightarrow (q \wedge \sim q)$ is

The dual of the statement pattern $(p \land \sim q) \to (q \land \sim p)$ is equivalent to

Let $p, q, r$ be three logical statements. Consider the compound statements $S_{1}: ((\sim p) \vee q) \vee ((\sim p) \vee r)$ and $S_{2}: p \rightarrow (q \vee r)$. Then,which of the following is $NOT$ true?

Let the operations $*, \odot \in \{\wedge, \vee\}$. If $(p * q) \odot (p \odot \sim q)$ is a tautology,then the ordered pair $(*, \odot)$ is:

Which of the following statements is a tautology?

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