UGC NET CSE | December 2013 | Part 2 | Question: 33

Question

The sum of products expansion for the function $F(x,y,z)=(x+y)\overline{z}$ is given as

• A. $\overline{x}\;\overline{y}z + x y \overline{z} + \overline{x}y \overline{z}$
• B. $xyz+xy\overline{z}+ x\overline{y}\; \overline{z}$
• C. $x\overline{y}\;\overline{z}+ \overline{x}\;\overline{y}\;\overline{z}+ xy\overline{z}$
• D. $xy\overline{z}+x\overline{y}\;\overline{z}+\overline{x}y\overline{z}$

Answer 1

(x+y)$\bar z$

=(x$\bar z$+y$\bar z$)

=$x(y+\bar y)\bar z + (x+\bar x) y \bar z$

=$xy\bar z+ x \bar y\bar z + xy\bar z + \bar x y \bar z$

=$xy\bar z+ x \bar y\bar z + \bar x y \bar z$

Hence,Option(D)$xy\bar z+ x \bar y\bar z + \bar x y \bar z$.

Answer 2

Ans is option (D)

xyz' + xy'z' +x'yz'

z'(xy + x'y + xy')

z' (xy'+ y)   [xy + x'y = y(x +x') = y]

xz'(z+y)