Symmetric difference

The symmetric difference between two sets A and B (denoted AΔB) is given as: $A\Delta B=(A\backslash B)\cup (B\backslash A)$. 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:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A\Delta (C\backslash B) = (A\Delta C)\backslash B }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A\Delta \cup_{i\in I} B_i = \cup_{i\in I} A\Delta B_i }

$A\Delta \cap _{i\in I}B_{i}=\cap _{i\in I}A\Delta B_{i}$

$A\Delta (B\Delta C)=(A\Delta B)\cap (A\Delta C)$

Symmetric differences are used to create filters for forcing constructions.