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Match List-I with List-II : List-IList-II (a) \(\bar{z}\) \(+ x\bar{y}\bar{z}\) \(+ \bar{x}yz\) \(+…

The matching is a-iii, b-i, c-iv, d-ii. Boolean absorption reduces (a) to \(\bar z+\bar x y\), while (b) reduces to \(\bar y+\bar x z\). Expression (c) is true for every…

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Match List-I with List-II :

List-IList-II
(a) zˉ\bar{z} +xyˉzˉ+ x\bar{y}\bar{z} +xˉyz+ \bar{x}yz +xˉyˉzˉ+ \bar{x}\bar{y}\bar{z}(i) yˉ+xˉz\bar{y} + \bar{x}z
(b) xˉyz\bar{x}yz +xˉyˉz+ \bar{x}\bar{y}z +xˉyˉzˉ+ \bar{x}\bar{y}\bar{z} +xyˉz+ x\bar{y}z +xyˉzˉ+ x\bar{y}\bar{z}(ii) xzˉ+xˉyˉx\bar{z} + \bar{x}\bar{y}
(c) xyzxyz +xyzˉ+ xy\bar{z} +xyˉz+ x\bar{y}z +xyˉzˉ+ x\bar{y}\bar{z} +xˉyz+ \bar{x}yz +xˉyˉz+ \bar{x}\bar{y}z +xˉyˉzˉ+ \bar{x}\bar{y}\bar{z}(iii) zˉ+yˉzˉ+xˉyz\bar{z} + \bar{y}\bar{z} + \bar{x}yz
(d) xyzˉxy\bar{z} +xyˉzˉ+ x\bar{y}\bar{z} +xˉyˉz+ \bar{x}\bar{y}z +xˉyˉzˉ+ \bar{x}\bar{y}\bar{z}(iv) yˉ+z+x\bar{y} + z + x
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Answer and explanation

Correct answer C

The matching is a-iii, b-i, c-iv, d-ii. Boolean absorption reduces (a) to zˉ+xˉy\bar z+\bar x y, while (b) reduces to yˉ+xˉz\bar y+\bar x z. Expression (c) is true for every input except x = 0, y = 1, z = 0, so it equals x+yˉ+zx+\bar y+z; (d) groups into xzˉ+xˉyˉx\bar z+\bar x\bar y.

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