Question:
The Boolean expression \( \overline{A + B + \overline{C}} \) is equal to:
The Boolean expression \( \overline{A + B + \overline{C}} \) is equal to:
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Apply De Morgan's Law carefully: \( \overline{A + B} = \overline{A} \cdot \overline{B} \)
Updated On: May 26, 2025
- \( \overline{A} + \overline{B} + C \)
- \( \overline{A} + \overline{B} + \overline{C} \)
- \( \overline{\overline{A} \cdot \overline{B} \cdot C} \)
- \( \overline{A} \cdot B + \overline{C} \)
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The Correct Option is C
Solution and Explanation
Using De Morgan’s Theorem:
\[
\overline{A + B + \overline{C}} = \overline{A} \cdot \overline{B} \cdot C
\Rightarrow \text{Double complement: } \overline{\overline{\overline{A} \cdot \overline{B} \cdot C}} = \overline{\overline{A} \cdot \overline{B} \cdot C}
\]
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