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For every A, B, and C, we have:
A intersection (B union C) = (A intersection B) union (A intersection C), A union (B intersection C) = (A union B) intersection (A union C);
A union (A intersection B) = A, A intersection (A union B) = A;
C\(A union B) = C\A intersection C\B, C\(A intersection B) = C\A union C\B.