Although option rejection is good approach. But 4 variable k-map could be used to find all solutions(means cells where one will come for all expression) like 1010 is also a solution.

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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:

- $0 \ 1 \ 0 \ 0$
- $1 \ 1 \ 0 \ 1$
- $1 \ 0 \ 1 \ 1$
- $1 \ 0 \ 0 \ 0$

+20 votes

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