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Difference between bags and sets

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• Caveat: Algebraic Laws can differ for bags and sets
  • Example of an Algebraic Law that holds for set, but not for bags:

    We know from Set Theory that: A ∩Set ( B ∪Set C ) = (A ∩Set B) ∪Set (A ∩Set C) But, this law does not hold for bags: A = { x } B = { x } C = { x } A ∩Bag ( B ∪Bag C ) = {x} ∩Bag ( {x} ∪Bag {x} ) = {x} ∩Bag {x,x} = {x} (A ∩Bag B) ∪Bag (A ∩Bag C) = ({x} ∩Bag {x}) ∪Bag ({x} ∩Bag {x}) = {x} ∪Bag {x} = {x,x}