Question

Symbolic form of the given switching circuit is equivalent to .............

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

Answer 1

Answer: (D)

$\sim (p\leftrightarrow q)$

Let $p:$ $S_1$ is closed

$q:$ $S_2$ is closed

From the circuit we get

$(p\wedge \sim q)\vee (\sim p\wedge q)$

$=\sim (\sim p\vee q)\vee \sim (p\vee \sim q)$

$=\sim \left[\right(\sim p\vee q)\wedge (p\vee \sim q\left)\right]$

$=\sim \left[\right(p\to q)\wedge (q\to p\left)\right]$

$=\sim (p\leftrightarrow q)$