Question

For the circuits shown below, the Boolean polynomial is

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

Answer 1

The correct option is D

$\left(~p\wedge q\right)\vee \left(p\wedge ~q\right)$

Boolean Polynomial

1. The component connected in series is represented by the symbol $\left(\wedge \right)$

1. The component connected in parallel is represented by the symbol $\left(\vee \right)$

According to the circuit,

$~p$and $q$ are connected in series so boolean polynomial is $\left(~p\wedge q\right)$,

Again, $p$and $~q$ are connected in series so boolean polynomial is $\left(p\wedge ~q\right)$,

And $\left(~p\wedge q\right)$ and $\left(p\wedge ~q\right)$ are connected in parallel so boolean polynomial is $\left(~p\wedge q\right)\vee \left(p\wedge ~q\right)$

So the boolean polynomial for the given circuit will be $\left(~p\wedge q\right)\vee \left(p\wedge ~q\right)$

Hence, the correct option is $\text{'}D\text{'}$.