The GATE Grind

GATE 2025 IN – Question 29

Digital Electronics · Number systems and combinational logic · 1 mark · Multiple choice

A Boolean function is $X=\bar A\bar B+\bar A\bar C$. The reduced form of $\bar X$ is

  1. $\bar A+\bar B+\bar C$
  2. $A+BC$
  3. $\bar A+B+C$
  4. $B+AC$

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Show answer and explanation

Correct answer: (B) $A+BC$

Explanation

Factor $X=\bar A(\bar B+\bar C)$.

By De Morgan’s law, $\bar X=A+\overline{\bar B+\bar C}=A+BC$.

The correct option is **B**.

Preserve the overbars when simplifying.