UGC NET CSE | December 2018 | Part 2 | Question: 11

Question

Consider the following boolean equations:

1. $wx+w(x+y)+x(x+y)=x+wy$
2. $(w \overline{x}(y+x \overline{z})+ \overline{w} \overline{x})y= \overline{x}y$

What can you say about the above equations ?

• A. (i) is true and (ii) is false
• B. (i) is false and (ii) is true
• C. Both (i) and (ii) are true
• D. Both (i) and (ii) are false

Answer 1

$1\,)\,wx+w(x+y)+x(x+y)$

      $=wx+wx+wy+x+xy$

      $=wx+wy+x(1+y)=wx+wy+x$

      $=x(1+w)+wy=x+wy$

So, $1$ is true.

$2\,)\,(w\bar{x}(y+x\bar{z})+\bar{w}\,\bar{x})y$

       $=(w\bar{x}y+wx\bar{x}\bar{z}+\bar{w}\bar{x})y$

       $=(\bar{x}(\bar{w}+wy)+0)y\,\,\,\left \{A\,\bar{A}=0\right \}$

       $=(\bar{x}(\bar{w}+y))y\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left \{A+\bar{A}B=A+B\right \}$

       $=\bar{x}\bar{w}y+\bar{x}y=\bar{x}y(\bar{w}+1)$

       $=\bar{x}y$

So, $2$ is true

$C$ should be the answer