Question

The Boolean expression \( \overline{A + B + \overline{C}} \) is equal to:

• A. \( \overline{A} + \overline{B} + C \)
• B. \( \overline{A} + \overline{B} + \overline{C} \)
• C. \( \overline{\overline{A} \cdot \overline{B} \cdot C} \)
• D. \( \overline{A} \cdot B + \overline{C} \)

Hint:

Apply De Morgan's Law carefully: \( \overline{A + B} = \overline{A} \cdot \overline{B} \)

Answer 1

The Correct Option is C

Using De Morgan’s Theorem: \[ \overline{A + B + \overline{C}} = \overline{A} \cdot \overline{B} \cdot C \Rightarrow \text{Double complement: } \overline{\overline{\overline{A} \cdot \overline{B} \cdot C}} = \overline{\overline{A} \cdot \overline{B} \cdot C} \]