Set Theory Laws

Vocabulary flashcards covering ten fundamental laws of set theory, including mathematical statements for union and intersection as provided in the lecture notes.

Commutative Law

A law stating that the order of sets in a operation does not change the result: $A \cup B = B \cup A$ and $A \cap B = B \cap A$.

Associative Law

A law stating that the grouping of sets in an operation does not change the result: $(A \cup B) \cup C = A \cup (B \cup C)$ and $(A \cap B) \cap C = A \cap (B \cap C)$.

Distributive Law

A law describing how union and intersection interact: $A \cap (B \cup C) = (A \cap B) \cup (A \cap C)$ and $A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$.

Identity Law

A law stating that the union of a set with the empty set or intersection with the universal set results in the set itself: $A \cup \emptyset = A$ and $A \cap U = A$.

Domination Law

A law stating that the union with the universal set results in the universal set, and intersection with the empty set results in the empty set: $A \cup U = U$ and $A \cap \emptyset = \emptyset$.

Idempotent Law

A law stating that performing a union or intersection on a set with itself results in the original set: $A \cup A = A$ and $A \cap A = A$.

Complement Law

A law describing the relationship between a set and its complement: $A \cup A' = U$ and $A \cap A' = \emptyset$.

Double Complement Law

A law stating that the complement of a set's complement is the original set: $(A')' = A$.

De Morgan Law

A law relating the complement of a union or intersection to the intersection or union of the complements: $(A \cup B)' = A' \cap B'$ and $(A \cap B)' = A' \cup B'$.

Absorption Law

A law stating that for any two sets $A$ and $B$: $A \cup (A \cap B) = A$ and $A \cap (A \cup B) = A$.