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According to the Principle of Duality, the Boolean equation will be equivalent to:
According to the Principle of Duality, the Boolean equation
$A + B' \cdot C + A' \cdot B \cdot C' = (A' + 0) \cdot (B + 1)$ will be equivalent to:
- (a)$(A \cdot B + C) \cdot (A' + (B + C')) = (A' \cdot 1) + (B \cdot 0)$
- (b)$(A \cdot B') + C \cdot (A' + B + C') = (A + 1) \cdot (B' + 0)$
- (c)$A \cdot (B' + C) \cdot (A' + B + C') = (A' \cdot 1) + (B \cdot 0)$
- (d)$(A \cdot B' \cdot C' + A \cdot B + A' \cdot C) = (B' \cdot 1) \cdot (A \cdot 0)$
Answer
Answer
AICorrect option: (c)
Answer: (c) $A \cdot (B' + C) \cdot (A' + B + C') = (A' \cdot 1) + (B \cdot 0)$
By the Principle of Duality, every $+$ is replaced by $\cdot$, every $\cdot$ by $+$, and every $0$ by $1$ (and vice versa), while the variables/complements are left unchanged. Applying this to $A + B'\cdot C + A'\cdot B\cdot C' = (A'+0)\cdot(B+1)$ gives $A\cdot(B'+C)\cdot(A'+B+C') = (A'\cdot 1)+(B\cdot 0)$, which is option (c).
From ISC 2026 Improvement Computer Science Paper 1, question 1(ii).