3. If S 1 and S 2 are finite sets, show that |S 1 × S 2 | = |S 1 ||S 2 |.
4. Consider the relation between two sets defined by S l = S 2 if and only if |S 1 | =
|S 2 |. Show that this is an equivalence relation.
5. Prove DeMorgan's laws, Equations (1.2) and (1.3).
6. Occasionally, we need to use the union and intersection symbols in a manner
analogous to the summation sign ∑. We define
with an analogous notation for the intersection of several sets.
With this notation, the general DeMorgan's laws are written as
and
Prove these identities when P is a finite set.
7. Show that
8. Show that S l = S 2 if and only if
9. Show that
10. Show that the distributive law