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Match List I with List II. List IList II A. x·(y+0) I. (x̄+0)·(ȳ·z) B. x̄·1+(ȳ+z) II. x+y·1 C.…

The dual of a Boolean expression is found by exchanging AND (·) with OR (+) and 0 with 1, leaving the variables and their complements unchanged. Thus \(x \cdot (y + 0)\) has…

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Match List I with List II.

List IList II
A. x·(y+0)I. (x̄+0)·(ȳ·z)
B. x̄·1+(ȳ+z)II. x+y·1
C. x̄·(ȳ+0)III. x̄+ȳ·1
D. x·1+(y+z̄)IV. (x+0)·(y·z̄)
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Answer and explanation

Correct answer C

The dual of a Boolean expression is found by exchanging AND (·) with OR (+) and 0 with 1, leaving the variables and their complements unchanged. Thus x⋅(y+0)x \cdot (y + 0) has the dual x+y⋅1x + y \cdot 1 (II); xˉ⋅1+(yˉ+z)\bar{x} \cdot 1 + (\bar{y} + z) has the dual (xˉ+0)⋅(yˉ⋅z)(\bar{x} + 0) \cdot (\bar{y} \cdot z) (I); xˉ⋅(yˉ+0)\bar{x} \cdot (\bar{y} + 0) has the dual xˉ+yˉ⋅1\bar{x} + \bar{y} \cdot 1 (III); and x⋅1+(y+zˉ)x \cdot 1 + (y + \bar{z}) has the dual (x+0)⋅(y⋅zˉ)(x + 0) \cdot (y \cdot \bar{z}) (IV).

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  • UGC NET Computer Science and Applications

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