Theorem 5.20

Basic Properties

$(A^c)^c = A$ and $A - B = A \cap B^c$

Empty Set and Universal Set

$A - \emptyset = A$ and $A - U = \emptyset$; $\emptyset^c = U$ and $U^c = \emptyset$

De Morgan's Laws

$(A \cap B)^c = A^c \cup B^c$ and $(A \cup B)^c = A^c \cap B^c$

Subsets and Complements

$A \subseteq B$ if and only if $B^c \subseteq A^c$