The logical statement $(p \lor q) \land [(\sim p \land q) \lor (p \land \sim q)] \land \sim q$ is logically equivalent to

The simplified switching circuit for the following circuit is (Assume the circuit consists of two switches $S_1$ and $S_2$ in parallel, connected in series with a switch $S_3$):

Let $p, q, r$ be three statements,then $[p$ $\rightarrow (q$ $\rightarrow r)] \leftrightarrow [(p \wedge q)$ $\rightarrow r]$ is

For the circuit shown below,the Boolean polynomial is

Which of the following sentences are statements? Give reasons for your answer.
The sum of $5$ and $7$ is greater than $10.$

For each of the following compound statements,first identify the connecting words and then break it into component statements.
$x=2$ and $x=3$ are the roots of the equation $3x^{2} - x - 10 = 0$.