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Basic Laws of Boolean Algebra

Name Equation(s)
Commutative x∧y = y∧x
x∨y = y∨x
Associative x∧(y∧z) = x∧y∧z
x∨(y∨z) = x∨y∨z
Distributive x∧(y∨z) = (x∧y)∨(x∧z)
x∨(y∧z) = (x∨y)(x∨z)
Idempotent x∧x = x
x∨x = x
Double negative ¬¬x = x
Complementary x∧¬x = 0
x∨¬x = 1
Intersection x∧1 = x
x∧0 = 0
Union x∨1 = 1
x∨0 = x
De Morgan's ¬(x∧y) = ¬x∨¬y
¬(x∨y) = ¬x∧¬y
Absorption x(x∨y) = x∨(x∧y) = x
Identity x∧1 = x
x∨0 = x