Chapter 6.4, Problem 11ES

To determine

(a)

To prove:

Show that the elements of S satisfies:

1. The commutative law for $+$
2. The commutative law for $\cdot$
3. The associative law for $+$
4. The associative law for $\cdot$
5. The distributive law for + over $\cdot$
6. The distributive law for $\cdot$ over +

To determine

(b)

To prove:

0 is an identity element for + and that 1 is an identity element for $\cdot$.

To determine

(c)

To prove:

For every a in S, $a+\overline{a}=1\text{ and }a\cdot \overline{a}=0$.