Consider the following statements p : the switch $\mathrm{S}_1$ is closed. q : the switch $\mathrm{S}_2$ is closed. $r$ : the switch $\mathrm{S}_3$ is closed. Then the switching circuit represented by the statement $(\mathrm{p} \wedge \mathrm{q}) \vee(\sim \mathrm{p} \wedge(\sim \mathrm{q} \vee \mathrm{p} \vee \mathrm{r}))$ is

• A

  
  
• B

  
  
• Correct answer
  C

  
  
• D

  
  

Solution

Let \(p\) : the switch \(S_1\) is closed \(q\) : the switch \(S_2\) is closed \(r\) : the switch \(S_3\) is closed \(\sim p\) : the switch \(S_1^{\prime}\) is closed or the switch \(S_1\) is open \(\sim q\) : the switch \(S_2^{\prime}\) is closed or the switch \(S_2\) is open \(\sim r\) : the switch \(S_3^{\prime}\) is closed or the switch \(S_3\) is open The switching circuit corresponding to the given statement pattern is given::

Hence, the correct answer is option: 'C'.