The statement pattern $\sim(p \vee q) \vee(\sim p \wedge q)$ is equivalent to

Statement-$I$: $\sim (p \leftrightarrow q)$ is equivalent to $(p \wedge \sim q) \vee (q \wedge \sim p)$.
Statement-$II$: $p$ $\rightarrow (p$ $\rightarrow q)$ is a tautology.

Write the contrapositive and converse of the following statement:
"You cannot comprehend geometry if you do not know how to reason deductively."

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

Consider the statement patterns:
$A. (q \to p) \lor (p \to q)$
$B. (\sim p \lor \sim q) \leftrightarrow \sim (p \land q)$
$C. [(p \lor q) \land \sim p] \land \sim q$
$D. (p \land q) \land (\sim p \lor \sim q)$
Then identify the nature of these statement patterns.

The statement $A$ $\rightarrow (B$ $\rightarrow A)$ is equivalent to