Question

The negation of compound statement $\left(p \land q\right)\Leftrightarrow \left(r \land q\right)$ is equivalent to

• A. $\left[\left(p \land q\right) \lor \left(q \land r\right)\right]\land \left[\sim \left(p \land q \land r\right)\right]$
• B. $\left(\right.p\land q\land r\left.\right)\lor \left[\right.\left(\right.p\land q\left.\right)\lor \left(\right.q\land r\left.\right)\left]\right.$
• C. $\sim \left(p \land q \land r\right)\lor \left[\left(p \land q\right) \lor \left(q \land r\right)\right]$
• D. none of these

Answer 1

Answer: (A)

$\left(p \land q\right)\Leftrightarrow \left(r \land q\right)$ is equivalent to
$\left[\sim \left(p \land q\right) \lor \left(r \land q\right)\right]\land \left[\sim \left(r \land q\right) \lor \left(p \land q\right)\right]$