identity laws of algebra of sets
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The empty set has no members, and the universe set has all possible members (in a particular context). Identity laws: ... The identity laws (together with the commutative laws) say that, just like 0 and 1 for addition and multiplication, Ø and U are the identity elements for union and intersection, respectively.
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The Law Of Algebra Of Sets:
Commutative Law:
A U B = B U A
A∩B
Associative Law:
(A U B) U C = A U (B U C)
(A ∩ B) ∩ C = A ∩ (B ∩ C)
Idempotent Sets:
A U A = A
A ∩ A = A
Distributive Laws:
(A U B) ∩ C = (A ∩ C) U (B ∩ C)
(A ∩ B) U C = (A ∩ C) U (B U C)
A U (B ∩ C) (A U B) ∩ (A U C)
A ∩ (B U C) = (A ∩ B) U (A U C)
De Morgan's Law:
(A U B) = A ∩ B
(A ∩ B) = A U B
(A U B U C) = A ∩ B ∩ C
A ∩ B ∩ C= A U B U C
Identity Laws:
A U Ф = A
A ∩ Ф = Ф
A U u = u
A ∩ u = A
Compliment Laws:
A U A = u
A ∩ A = Ф
Involution Laws:
(A) = A
Ф = u
u = Ф