Consider the Boolean expression over two Boolean variables and . Which one of the following Boolean expressions is equivalent to the given Boolean expression ?

Explanation: Logic De Morgan's First Law: Apply the rule where and . De Morgan's Second Law: Apply the rule to the first term. Final Form: Final Equation

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NIMCET 2025 — Computer PYQ

NIMCET | Computer | 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 $X$ ?

Choose the correct answer:

A.
$\overset{ˉ}{A} . \overset{ˉ}{B} + C$
B.
$\overline{A . C} + \overline{B . C}$

Correct Answer:

$\overline{A . \overset{ˉ}{B}} + \overset{ˉ}{C}$

Explanation

Logic

De Morgan's First Law:

Apply the rule $\overline{P \cdot Q} = \bar{P} + \bar{Q}$ where $P = (A + B)$ and $Q = C$ .

$X = \overline{(A+B)} + \bar{C}$
De Morgan's Second Law:

Apply the rule $\overline{A + B} = \bar{A} \cdot \bar{B}$ to the first term.

$X = (\bar{A} \cdot \bar{B}) + \bar{C}$
Final Form:

$X = \bar{A} \bar{B} + \bar{C}$

Final Equation

\overline{(A+B) \cdot C} = \overline{(A+B)} + \bar{C} = (\bar{A} \cdot \bar{B}) + \bar{C}

Explanation

Logic

De Morgan's First Law:

Apply the rule $\overline{P \cdot Q} = \bar{P} + \bar{Q}$ where $P = (A + B)$ and $Q = C$ .

$X = \overline{(A+B)} + \bar{C}$
De Morgan's Second Law:

Apply the rule $\overline{A + B} = \bar{A} \cdot \bar{B}$ to the first term.

$X = (\bar{A} \cdot \bar{B}) + \bar{C}$
Final Form:

$X = \bar{A} \bar{B} + \bar{C}$

Final Equation

\overline{(A+B) \cdot C} = \overline{(A+B)} + \bar{C} = (\bar{A} \cdot \bar{B}) + \bar{C}

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TopicAll "Boolean Algebra" PYQs →SubjectMore Computer Questions →YearNIMCET 2025 Paper →All NIMCET Questions →

C.
$\overline{A . \overset{ˉ}{B}} + \overset{ˉ}{C}$
(Correct Answer)

D.
$\overset{ˉ}{A} + \overline{B . \overset{ˉ}{C}}$

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