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Set Identities

For every A, B, and C, we have:

• Distributivity

  A intersection (B union C) = (A intersection B) union (A intersection C),

  A union (B intersection C) = (A union B) intersection (A union C);

• Cancellation

  A union (A intersection B) = A,

  A intersection (A union B) = A;

• De Morgan

  C\(A union B) = C\A intersection C\B,

  C\(A intersection B) = C\A union C\B.