# Symmetric difference

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The **symmetric difference** between two sets A and B (denoted AΔB) is given as:
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This operator is symmetric in that AΔB=BΔA. Also, AΔA is the empty set, while the symmetric difference of the empty set with any set is that set.

The set-theoretic operator Δ obeys several laws:

Symmetric differences are used to create filters for forcing constructions.