Fundamental laws of set algebra

\bar{\bar{A}} = A

\bar{\emptyset} = Ω

\bar{Ω} = \emptyset

A \cup \emptyset = A

A \cap Ω = A

A \cup Ω = Ω

A \cap \emptyset = A

Commutative laws

A \cup B = B \cup A

A \cap B = B \cap A

Associative laws

(A \cup B) \cup C = A \cup (B \cup C)

(A \cap B) \cap C = A \cap (B \cap C)

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)

Absorption laws

A \cup (A \cap B) = A

A \cap (A \cup B) = A

Idempotent laws

A \cup A = A

A \cap A = A

De Morgan's laws

\bar{A \cup B} = \bar{A} \cap \bar{B}

\bar{A \cap B} = \bar{A} \cup \bar{B}

Keywords:

General Information
Symbols, and relationships in mathematics
Number theory
Number Sets
Prime Numbers - Prime Factorization
Divisibility Rules
Greatest Common Divisor (factor) - Least Common Multiple
Operations with rational numbers
Binomial theorem
Binomial theorem
Combinatorics
Permutations
Combination
Variation
Sets
Operations on Sets
Cardinality of sets
Fundamental laws of set algebra
Cartesian product
Relation
Logic
Logical Operations and Truth Tables
Properties of Logical Operators
Graph Theory
Graph Theory - definitions, relationships