Simplify Boolean Expression

Question

so I have this expression and I have to simplify it to minimum SoPs

$(x+(y'(z+w)')')'$

so my final answer is $x'y'z'w'$

but I think there is something wrong or trick can some one help me or tell me if my answer is right or wrong .

thank you

Answer 1

Your answer is correct. Using DeMorgan's theorem:

$$(X + (Y^{'} \cdot (Z + W)^{'})^{'})^{'} $$

$$= (X + (Y + (Z + W))^{'}$$

$$= (X + Y + Z + W)^{'}$$ $$= X^{'} Y^{'} Z^{'}W^{'}$$