# Using de Morgan's law to complement boolean expression

Using de Morgan's Law, write an expression for the complement of F if F(x, y, z) = xy + x'z + yz' .

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#### Solution Preview

In the following solution, ' is used to indicate the complement.

F'(x,y,z) = (xy + x'z + yz')'

= (xy + x'z)'(yz')' -- Using (A + B)' = A'B'

= (xy)'(x'z)'(yz') -- Using (A + B)' = A'B'

= (x' + y')((x')' + z')(y' + (z')') -- Using (AB)' = A' + B'

= (x' + ...

#### Solution Summary

Wherever applicable, solution mentions the law used to arrive at current step from previous step.

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