Question

Simplify the following circuit and find the boolean polynomial

• A. $p\vee (q\wedge r)$
• B. $p\wedge (q\vee r)$
• C. $p\vee (q\vee r)$
• D. $p\wedge (q\wedge r)$

Answer 1

The correct option is A

$p\vee (q\wedge r)$

Step 1: Given figure

Step 2: Simplify the circuit

The current will be passed through the first box if anyone of $p$ or $q$ will be closed. It means, $(p\vee q)$

Similarly, the current will be passed from the second box if anyone of $p$ or $r$ will be closed. So, $(p\vee r)$

And the current will flow through both the box if both the box will be closed. So,

$$\begin{gathered} (p\vee q)\wedge (p\vee r) \\ p\vee \left(q\wedge r\right) \end{gathered}$$

Hence, option (A) is the correct answer.