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 $X$?
๐ฅ Video solution / Text Solution of this question is given below:
We are given the Boolean expression:
$X = \overline{(A + B)\cdot C}$
First apply De-Morganโs Law:
$\overline{(A + B)\cdot C} = \overline{(A + B)} + \overline{C}$
Again apply De-Morganโs Law on
$\overline{(A + B)}$= $ \overline{A}\cdot \overline{B}$
So,
$X = (\overline{A}\cdot \overline{B}) + \overline{C}$
This matches option (2):
$\overline{A\cdot B} + \overline{B\cdot C}$
Commented Feb 11, 2026
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