Question:
According to De Morgan's theorem, \(\overline{A+B}\) is equal to
According to De Morgan's theorem, \(\overline{A+B}\) is equal to
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De Morgan's theorem changes OR to AND and AND to OR after complementing each variable.
Updated On: May 27, 2026
- \(\overline{A}+\overline{B}\)
- \(\overline{A}\,\overline{B}\)
- \(AB\)
- \(A+B\)
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The Correct Option is B
Solution and Explanation
Concept:
De Morgan's theorem is used to simplify complemented Boolean expressions.
Step 1: The theorem states: \[ \overline{A+B}=\overline{A}\cdot\overline{B} \]
Step 2: It means the complement of OR operation becomes AND operation of complements.
Step 3: Therefore: \[ \overline{A+B}=\overline{A}\,\overline{B} \] Hence: \[ \boxed{\overline{A}\,\overline{B}} \]
Step 1: The theorem states: \[ \overline{A+B}=\overline{A}\cdot\overline{B} \]
Step 2: It means the complement of OR operation becomes AND operation of complements.
Step 3: Therefore: \[ \overline{A+B}=\overline{A}\,\overline{B} \] Hence: \[ \boxed{\overline{A}\,\overline{B}} \]
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