TABLE 1 Set Identities. Identity $A \cap U = A$ $A \cup \emptyset = A$ $A \cup U = U$ $A \cap \emptyset = \emptyset$ $A \cup A = A$ $A \cap A = A$ $\overline{(A)} = A$ $A \cup B = B \cup A$ $A \cap B = B \cap A$ $A \cup (B \cup C) = (A \cup B) \cup C$ $A \cap (B \cap C) = (A \cap B) \cap C$ $A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$ $A \cap (B \cup C) = (A \cap B) \cup (A \cap C)$ $\overline{A \cap B} = \overline{A} \cup \overline{B}$ $\overline{A \cup B} = \overline{A} \cap \overline{B}$ $A \cup (A \cap B) = A$ $A \cap (A \cup B) = A$ $A \cup \overline{A} = U$ $A \cap \overline{A} = \emptyset$ Name Identity laws Domination laws Idempotent laws Complementation law Commutative laws Associative laws Distributive laws De Morgan's laws Absorption laws Complement laws
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