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

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.

In a switching circuit, if the combination $(S_1 \land S_2)$ is connected in parallel to the combination $(S'_1 \land S'_2)$, then the room is lit only when ...

Find the component statements of the following and check whether they are true or not.
$A$ square is a quadrilateral and its four sides are equal.

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

Check the validity of the statement given below by the method specified against it.
$p:$ The sum of an irrational number and a rational number is irrational (by contradiction method).