Question

The symbolic form of logic of the circuit given below is

• A. \([\,(p\wedge q')\vee p'\,]\wedge q\)
• B. \([\,p\vee(q'\cdot p')\,]\vee q\)
• C. \([\,(p\wedge p')\vee q'\,]\wedge q\)
• D. \(p\wedge(p\vee p')\vee q\)

Hint:

To write logic from diagrams: \textbf{trace NOT → AND → OR → final AND} in the same order shown.

Answer 1

The Correct Option is A

Step 1: Examine the diagram conceptually. The circuit shows the following gate sequence: - Input \(p\) goes to a NOT gate → \(p'\). - Input \(q\) goes to a NOT gate → \(q'\).
Step 2: The upper branch combines \(p\) with \(q'\) using an AND operation as per diagram marking: \[ H_1 = p\wedge q'. \]
Step 3: This output \(H_1\) is joined with \(p'\) through an OR gate: \[ H_2 = (p\wedge q') \vee p'. \]
Step 4: The final stage ANDs \(H_2\) with \(q\): \[ F = [\,(p\wedge q')\vee p'\,]\wedge q. \]
Step 5: Compare options—only option (A) matches this exact Boolean trace. Hence → (A).