‹ Back to the paper
According to the Principle of duality, the Boolean equation will be equivalent to:
According to the Principle of duality, the Boolean equation
$(P + Q') \cdot R \cdot 1 = P \cdot R + Q' \cdot R$ will be equivalent to:
- (a)$P \cdot Q' + R + 1 = (P + R) \cdot (Q' + R)$
- (b)$P \cdot Q' + R + 0 = (P + R) \cdot (Q' + R)$
- (c)$P' \cdot Q + R + 1 = (P' \cdot R') \cdot (Q + R')$
- (d)$P \cdot Q' + R \cdot 0 = (P + R) \cdot (Q' + R)$
Answer
Answer
AICorrect option: (b)
Answer: (b) $P \cdot Q' + R + 0 = (P + R) \cdot (Q' + R)$
By the Principle of Duality, every $\cdot$ is replaced by $+$, every $+$ is replaced by $\cdot$, and every $1$ is replaced by $0$ (variables unchanged). Applying this to $(P+Q') \cdot R \cdot 1 = P \cdot R + Q' \cdot R$ gives $P \cdot Q' + R + 0 = (P + R) \cdot (Q' + R)$, which is option (b).
From ISC 2024 Specimen Computer Science Paper 1, question 1(iii).