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41 votes
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The simultaneous equations on the Boolean variables $x, y, z$ and $w$,

  • $x + y + z = 1 $
  • $xy = 0$
  • $xz + w = 1$
  • $xy + \bar{z}\bar{w} = 0$

have the following solution for $x, y, z$ and $w,$ respectively:

  1. $0 \ 1 \ 0 \ 0$
  2. $1 \ 1 \ 0 \ 1$
  3. $1 \ 0 \ 1 \ 1$
  4. $1 \ 0 \ 0 \ 0$
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5 Answers

Best answer
37 votes
37 votes

Take each option one by one and try to put the values of $x, y, z$ and $w$ in question:
1.

  • $0+1+0 =1$
  • $0.1 =0$
  • $0.0+0 =0$  (went wrong)      So, this is not the right option

2.

  • $1+1+0 =1$
  • $1.1 =1$ (went wrong)          not right

3 .

  • $1+0+1 =1$
  • $1.0 =0$
  • $1.1+1=1$
  • $1.0 +1.0 =0 $     This is the right option

Correct Answer: $C$

edited by
8 votes
8 votes
My approach option elimination:-
as xy=0
then x= or y= 0 or x and y both are 0. So B is eliminated.

xy+z'w'=0
implies these xy=0 and z'w' =0
implies these either z'=0 or w'=0 or both
impiles these either z=1 or w=1 or both.
So A and D are eliminated.

Answer is C
Answer:

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