Question

If $p \equiv$ The switch $S_1$ is closed, $q \equiv$ The switch $S_2$ is closed, $r \equiv$ switch $S_3$ is closed, then symbolic form of the switching circuit is equivalent to \dots

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

Hint:

Always look for the Absorption Law ($p \vee (p \wedge q) = p$ and $p \wedge (p \vee q) = p$) when dealing with logic circuit simplifications, as it is the most common way multiple switches collapse into a single variable.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
In switching circuits: (i) Parallel switches use the OR ($\vee$) operator, and (ii) Series switches use the AND ($\wedge$) operator.

Step 2: Formula Application:
Analyze the diagram (implied in original set): Usually, these problems involve a structure like $p \wedge (q \vee \sim q)$ or $(p \wedge q) \vee (p \wedge \sim q)$.

Step 3: Explanation:
Using the Distributive Law: $(p \wedge q) \vee (p \wedge \sim q) \equiv p \wedge (q \vee \sim q)$. Since $q \vee \sim q$ is a Tautology ($T$), $p \wedge T \equiv p$.

Step 4: Final Answer:
The circuit is equivalent to $p$.