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### EXERCISES

1.      1. Construct a truth table for the following:

1. a) yz + z(xy)

2. b) x(y′ + z) + xyz

3.   c) (x + y)(x′ + y) (Hint: This is from Example 3.7.)

2.      2. Construct a truth table for the following:

1. a) xyz + x(yz)′ + x′(y + z) + (xyz)′

2. b) (x + y′)(x′ + z′)(y′ + z′)

3.   3. Using DeMorgan’s Law, write an expression for the complement of F if F(x, y, z) = xy′(x + z).

4.      4. Using DeMorgan’s Law, write an expression for the complement of F if F (x, y, z) = (x′ + y)(x + z)(y′ + z)′.

5.   5. Using DeMorgan’s Law, write an expression for the complement of F if F (w, x, y, z) = xz′(xyz + x) + y(wz + x′).

6.      6. Using DeMorgan’s Law, write an expression for the complement of F if F (x, y, z) = xz′(xy + xz) + xy′(wz + y).

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