Leyes del Algebra de Conjunto

CONMUTATIVA
A ∪ B = B ∪ A
A ∩ B = B ∩ A


ASOCIATIVA
(A ∪ B) ∪ C = A ∪ (B ∪ C)
(A ∩ B) ∩ C = A ∩ (B ∩ C)


DISTRIBUTIVA
(A ∩ B) ∪ C = (A ∪ C) ∩ (B ∪ C)
(A ∪ B) ∩ C = (A ∩ C) ∪ (B ∩ C)


REDUCCIÓN
A ∪ (B ∩ A) = A
A ∩ (B ∪ A) = A



IDEMPOTENCIA
A ∪ A = A
 A ∩ A = A


IDENTIDAD
A ∪ ∅ = A
 A ∩ Re = A



ABSORCIÓN
A ∪ Re = Re
 A ∩ ∅  = ∅



TERCER EXCLUIDO
A ∪ Ac = Re



CONTRADICCIÓN
A ∩ Ac = ∅



INVOLUCIÓN
(Ac)c = A



MORGAN
(A ∪ B) c = Ac ∩ Bc
 (A ∩ B) c = Ac ∪ Bc




DIFERENCIA
A - B = (A ∩ B)c



DISTRIBUTIVA DE LA DIFERENCIA
A - ( B ∪ C ) = ( A - B ) ∪ ( A - C )
A - ( B ∩  C ) = ( A - B ) ∩ ( A - C )



COMPLEMENTO
Re c = 0
      ∅ = Re