Theorem 5.2.2 - Set Identities

Given any sets $A$, $B$, and $C$, the universal set $U$ and the empty set $\emptyset$:
1. Commutative laws:	$A \cap B = B \cap A$
	$A \cup B = B \cup A$
2. Associative laws:	$(A \cap B) \cap C = A \cap (B \cap C)$
	$(A \cup B) \cup C = A \cup (B \cup C)$
3. Distributive laws:	$A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$
	$A \cap (B \cup C) = (A \cap B) \cup (A \cap C)$
4. Intersection with U (Identity):	$A \cap U = A$
5. Double Complement law:	$(A')' = A$
6. Idempotent laws:	$A \cap A = A$
	$A \cup A = A$
7. De Morgan's laws:	$(A \cup B)' = A' \cap B'$
	$(A \cap B)' = A' \cup B'$
8. Union with U (Universals Bounds):	$A \cup U = U$
9. Absorption laws:	$A \cup (A \cap B) = A$
	$A \cap (A \cup B) = A$
10. Alternative Representation for Set Diff:	$A - B = A \cap B'$

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