Category:Symmetric Difference

From ProofWiki
Jump to navigation Jump to search


This category contains results about Symmetric Difference.
Definitions specific to this category can be found in Definitions/Symmetric Difference.


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

Definition 1

$S * T := \paren {S \setminus T} \cup \paren {T \setminus S}$


Definition 2

$S * T = \paren {S \cup T} \setminus \paren {S \cap T}$


Definition 3

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


Definition 4

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


Definition 5

$S * T := \set {x: x \in S \oplus x \in T}$