Set Identities

  A,B are sets; U=Universal Set; u is union; n is intersection; ' is complement
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  A u {} = A                          Identity Laws
  A n U = A
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  A u U   = U                         Domination Laws
  A n {} = {} 
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  A u  A = A                          Idempotent Laws
  A n A = A
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  A''  = A                             Complementation Law
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   A u B = B u A                      Commutative Laws
   A n B = B n A
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  (A u B) u C = A u (B u C)           Associativity Laws
  A n (B n C) = (A n B) n C
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  A u (B n C) = (A u B) n (A u C)     Distributive Laws
  A n (B u C) = (A n B) u (A n C)  
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  (A u B)' =  A' n  B'                   De Morgan's Laws
  (A n B)' =  A' u B'   
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  A u A' = U                           Complement Laws
  A n A' = {}