Question

What is dual of \(A + B(AC) + D\)?

• A. \(A(B + D)(AC)\)
• B. \(A + (B + AC)D\)
• C. \(A + (B + AC) + D\)
• D. \(A(B + AC)D\)

Hint:

Dual → swap AND and OR everywhere.

Answer 1

The Correct Option is D

Concept: Dual of a Boolean expression is obtained by:

• Replacing \(+\) with \(\cdot\)

• Replacing \(\cdot\) with \(+\)

• Constants 0 and 1 are interchanged (not needed here)

Step 1: Given expression \[ A + B(AC) + D \]

Step 2: Replace operations \[ + \rightarrow \cdot,\quad \cdot \rightarrow + \]

Step 3: Apply transformation \[ A \cdot [B + (A + C)] \cdot D \]

Step 4: Simplify expression \[ A(B + AC)D \]

Step 5: Conclusion \[ \boxed{A(B + AC)D} \]

Final Answer: \[ \boxed{(D)} \]