Aspire Faculty ID #12038 · Topic: NIMCET 2025 · Just now
NIMCET 2025

Consider the Boolean expression $ X = \overline{(A + B) \cdot C}$ over two Boolean variables $A$ and $B$. Which one of the following Boolean expressions is equivalent to the given Boolean expression $X$?

Solution

We are given the Boolean expression:
$X = \overline{(A + B)\cdot C}$ 

First apply De-Morgan’s Law: $\overline{(A + B)\cdot C} = \overline{(A + B)} + \overline{C}$ 

Again apply De-Morgan’s Law on 
$\overline{(A + B)}$= $ \overline{A}\cdot \overline{B}$ 
So, $X = (\overline{A}\cdot \overline{B}) + \overline{C}$
This matches option (2):
$\overline{A\cdot B} + \overline{B\cdot C}$

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DILSHAN ALAM
DILSHAN ALAM , Student
Commented Feb 11, 2026
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