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+17 votes

Let $f(w, x, y, z) = \sum {\left(0,4,5,7,8,9,13,15\right)}$. Which of the following expressions are NOT equivalent to $f$?

**P:** $x'y'z' + w'xy' + wy'z + xz$

**Q:** $w'y'z' + wx'y' + xz$

**R:** $w'y'z' + wx'y' + xyz+xy'z$

**S:** $x'y'z' + wx'y'+ w'y$

- P only
- Q and S
- R and S
- S only

+16 votes

Best answer

w'x' | w'x | wx | wx' | |
---|---|---|---|---|

y'z' | 1 | 1 | 1 | |

y'z | 1 | 1 | 1 | |

yz | 1 | 1 | ||

yz' |

So, minimized expression will be

$xz + w'y'z' + wx'y'$ which is Q. From the K-map, we can also get P and R. So, only S is NOT equivalent to $f$.

http://www.eecs.berkeley.edu/~newton/Classes/CS150sp98/lectures/week4_2/sld011.htm

+19 votes

Let me show u a very simple method

Let w =1 ,x =1 ,y=1 ,z=1 then the value of f is 1

consider each statement

x'y'z' + w' x y' +w y' z +x z = 0.0.0 + 0.1.0 + 1.0.1 + 1.1 =1

w' y' z' +w x' z' y' +x z = 0.0.0 +1.0.0 +1.1 =1

w' y' z' +w x' y' +x y z +x y' z =0.0.0 +1.0.0 +1.1.1 +1.0.1 =1

x' y' z' +w x' y' + w' y = 0.0.0 + 1.0.0 + 0.1 =0

So statement (d) is false because w=1 x=1 y=1 z=1 the value of f is 0 .

(d) does not contain the essential Minterms .

x′y′z′+w′xy′+wy′z+xz

x′y′z′+w′xy′+wy′z+xz

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