Question

The complement of $(A + B)$ is:

• A. $\bar{A} + \bar{B}$
• B. $\bar{A}\bar{B}$
• C. $A + B$
• D. $\bar{A}B$

Hint:

De Morgan: \((A+B)' = A'B'\), \((AB)' = A' + B'\)

Answer 1

The Correct Option is B

Concept: Use De Morgan’s Laws: \[ \overline{A + B} = \bar{A} \cdot \bar{B} \]

Step 1: Apply complement on sum. \[ (A + B)' = A' \cdot B' \]

Step 2: Interpret result.
• Complement of OR becomes AND of complements

Step 3: Match with options. \[ \bar{A}\bar{B} \]

Step 4: Conclusion. \[ \boxed{(2)} \]