Using DeMorgan's Law, find the correct expression for the complement of F if F(x,y,z) = xz' (xy + xz) + xy'(wz + y).
Solution:
To find the complement of F, we need to apply DeMorgan's Law, which states that the complement of a logical expression is obtained by negating each term and changing the logical operators.
First, let's break down the given expression:
F(x,y,z) = xz' (xy + xz) + xy'(wz + y)
Now, let's apply DeMorgan's Law to each term:
1. Negate xz':
The complement of xz' is (xz')'.
2. Negate (xy + xz):
The complement of (xy + xz) is (xy + xz)'.
3. Negate xy':
The complement of xy' is (xy')'.
4. Negate (wz + y):
The complement of (wz + y) is (wz + y)'.
Now, let's substitute the negated terms back into the original expression:
F(x,y,z) = (xz')' * (xy + xz)' + (xy')' * (wz + y)'
Finally, let's simplify the expression:
F(x,y,z) = (xz')' * (xy' * xz')' + (xy')' * (wz + y)'
And that is the correct expression for the complement of F using DeMorgan's Law.