Prove DeMorgan's Law and Counting Using Lists

1. Prove

Let A, B, and C be sets. Then

A - (B union C) = (A - B) intersection (A - C) and A - (B intersection C) = (A - B) union (A - C)

2. 1.) A U.S. Social Security number is a nine-digit number. The first digit(s) may be 0.

a.) How many SS numbers are available? 10^9

b.) How many of these are even?

c.) How many have all of their digits even? 5^9

d.) How many read the same backward and forward?

e.) How many have none of their digits equal to 8? 9^9

f.) How many have at least one digit equal to 8?

g.) How many have exactly one 8?