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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
$(1 + Y) \cdot (X + Y) = Y + X'$ will be equivalent to:
- (a)$(1 + Y') \cdot (X' + Y') = Y' + X$
- (b)$(0 \cdot Y) + (X \cdot Y) = Y \cdot X'$
- (c)$(0 + Y) \cdot (X + Y) = Y + X'$
- (d)$(1 \cdot Y) + (X \cdot Y) = Y \cdot X'$
Answer
Answer
AICorrect option: (b)
Answer: (b) $(0 \cdot Y) + (X \cdot Y) = Y \cdot X'$
By the Principle of Duality, every AND ($\cdot$) is replaced by OR ($+$), every OR by AND, and every 1 by 0 (0 by 1), while variables/complements stay unchanged. Applying this to $(1+Y) \cdot (X+Y) = Y+X'$ gives $(0 \cdot Y) + (X \cdot Y) = Y \cdot X'$.
From ISC 2025 Computer Science Paper 1, question 1(iii).