NIELIT Scientist B 2020 November: 97

Question

If $x, y, z$ are Boolean variable then $(x+\overline y)(x \cdot \overline y+x\cdot z)(\overline x\cdot \overline z+\overline y)$ is equal to :

• A. $x\cdot\overline y$
• B. $x\cdot\overline y+z$
• C. $x\cdot \overline z$
• D. none of the options

Answer 1

Given boolean expression $: (x+\bar y)(x\bar y+xz)(\bar x\bar z+\bar y)$

$\implies x\bar y+xz+x\bar y+x\bar yz)(\bar x\bar z+\bar y)\:\text{(Multiplying first 2 brackets)} \quad (\because A+A=A)$

 $\implies$ $(x\bar y+x\bar yz+xz)(\bar x\bar z+\bar y)$

$\text{Taking $x\bar y$ as common}$

$\implies (x\bar y(1+z)+xz)(\bar x\bar z)+\bar y \quad (\because 1+A=1)$

$\implies (x\bar y+xz)(\bar x\bar z+\bar y)$

$\implies x\bar y+x\bar yz$

$\implies x\bar y (1+z)$

$\implies x\bar y$

Option $(A)$ is correct.