Question

For the circuit show below, the Boolean polynomial is

• A. $ \left(\sim p \vee q\right)\vee\left(p \vee \sim q\right) $
• B. $ \left(\sim p \wedge q\right)\wedge\left(p \wedge q\right) $
• C. $ \left(\sim p \wedge\sim q\right)\wedge\left(q \wedge p\right) $
• D. $ \left(\sim p \wedge q\right)\vee\left(p \wedge \sim q\right) $

Answer 1

Answer: (D)

Since, $\sim p$ and $q$ both switch also are in series
$\Rightarrow (\sim p \wedge q)$...(i)
and $p$ and $\sim q$ both switch also are in series
$\Rightarrow (p \wedge \sim q)$...(ii)
Both Eqs. (i) and (ii) are parallel switch
$\Rightarrow (\sim p \wedge q) \vee(p \wedge \sim q)$