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closed with the note: duplicate
The simultaneous equations on the Boolean variables x, y, z and w,
  X+Y+Z=1

XY=0

XZ+W=1
have the following solution for x, y, z and w, respectively:
(a) 0 1 0 0 (b) 1 1 0 1 (c) 1 0 1 1 (d) 1 0 0 0
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Boolean Sum is represented by "OR". I think u know how OR works, when both inputs are 0 ,0 then only output is 0, otherwise output is 1.

so check out each option. I think option C will be correct

 X+Y+Z=1--------------------------------------------------(1)
 XY=0--------------------------------------------------------(2)
 XZ+W=1---------------------------------------------------(3)

option C says X: 1     Y: 0     Z: 1          W: 1

put these values in eq 1,2 and 3, it will satisfy..

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C option

If we put the options in the 3 equations only c option can satisfy all 3 equations.
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