Set Identities

• Set identities are a list of different set properties and laws used to prove the set operations, subsets, and equivalence.
• Set Identities - It is also called as set properties.
• List of set identities:

  • Identity Laws
  • Domination Laws
  • Idempotent Laws
  • Commutative Laws
  • Associative Laws
  • Distributive Laws
  • Complement Laws
  • Complementation/Involution Laws
  • Absorption Laws
  • De Morgan’s Laws
  • Set Difference Law
• Identity Laws

  • A U Ø = A
  • A ∩ U = A
• Domination Laws

  • A U U = U
  • A ∩ Ø = Ø
• Idempotent Laws

  • A U A = A
  • A ∩ A = A
• Commutative Laws

  • AUB=BUA
  • A ∩ B = B ∩ A
• Associative Laws

  • AU(BUC)=(AUB)UC
  • A∩(B∩C)=(A∩B)∩C
• Distributive Laws

  • A U (B ∩ C) = (A U B) ∩ (A U C)
  • A∩(BUC) = (A∩B)U(A∩B)
• Complement Laws

  • A U A’ = U
  • A ∩ A’ = Ø
• Complementation/Involution Laws

  • A’’ = A
  • U’ = Ø
  • Ø’ = U
• Absorption Laws

  • AU(A∩B)=A
  • A ∩ (A U B) = A
• De Morgan’s / Theorems Laws

  • (A ∩B)’ = A’ U B’
  • (A UB)’ = A’ ∩B’
• Set Theorem/Difference Laws

  • A - B = A ∩ B’