Useful operations or properties on sets are as given

• A U U = U
• A  ∩  Φ =  Φ
• ^ΦC = U
• U^C =  Φ

Algebra of Sets:

Idempotent Law: For any defined set A,

• A U A = A
• A ∩ A = A

Identity Law: For any defined set A,

• A U Φ  = A
• A ∩ U = A

Commutative Law: For any two sets A and B

• A  U  B = B  U  A
• A  ∩  B = B  ∩  A

Associative Law: For any three sets A, B and C

• (A U B) U C = A U (B U C)
• A ∩ (B ∩ C) = (A ∩ B) ∩ C

Distributive Law: For any three sets A, B and C

• A U (B ∩ C) = (A U B) ∩ (A U C)
• A ∩ (B U C) = (A ∩ B) U (A ∩ C)

De Morgan's Law: For any two sets A and B

• (A U B)' = A' ∩  B'
• (A ∩ B)' = A' U B'

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