Definition:Symmetric Difference/Definition 2

Definition
The symmetric difference between two sets $S$ and $T$ is written $S * T$ and is defined as:


 * $S * T = \left({S \cup T}\right) \setminus \left({S \cap T}\right)$

where:


 * $S \setminus T$ denotes set difference between $S$ and $T$, defined as $S \setminus T = \left\{{x: x \in S \land x \notin T}\right\}$
 * $S \cup T$ is the union of $S$ and $T$, defined as $S \cup T = \left\{{x: x \in S \lor x \in T}\right\}$
 * $S \cap T$ is the intersection of $S$ and $T$, defined as $S \cap T = \left\{{x: x \in S \land x \in T}\right\}$.

Also see

 * Equivalence of Definitions of Symmetric Difference