Category:Definitions/Symmetric Difference

From ProofWiki
Jump to navigation Jump to search

This category contains definitions related to Symmetric Difference.
Related results can be found in Category: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

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

Definition 5

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