Set Identities

Learn about the identities of sets and how they can be proved.

Commutativity

We know that the union and intersection operations are commutative. We also know that the set difference operation is not commutative. There’s a difference between keeping the elements of AA that are not in BB and keeping the elements of BB that are not in AA. Both sets can have elements that are not common. Therefore, we can say that ABBA{A\setminus B} \ne {B\setminus A}. But if we look at the symmetric difference, we can see that it’s commutative. This is because the union operation is commutative, as exhibited below:

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