Question

The statement pattern $\left(p\, \wedge\, q\right) \wedge \left[\sim\,r\, \vee \left(p\, \wedge\,q\right)\right] \vee \left(\sim p\,\wedge\,q\right)$ is equivalent t o ............

• A. $r$
• B. $q$
• C. $\left(p\, \wedge\, q\right) $
• D. $p$

Answer 1

Answer: (B)

We have, $(p \wedge q) \wedge[\sim r \vee(p \wedge q)] \vee(\sim p \wedge q)$
$ \equiv(p \wedge q) \vee(\sim p \wedge q)$
$\equiv(p \vee \sim p) \wedge q \equiv T \wedge q=q$