# Category:Symmetric Difference

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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 $S \symdif T$ and is defined as:

### Definition 1

- $S \symdif T := \paren {S \setminus T} \cup \paren {T \setminus S}$

### Definition 2

- $S \symdif T = \paren {S \cup T} \setminus \paren {S \cap T}$

### Definition 3

- $S \symdif T = \paren {S \cap \overline T} \cup \paren {\overline S \cap T}$

### Definition 4

- $S \symdif T = \paren {S \cup T}\cap \paren {\overline S \cup \overline T}$

### Definition 5

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

## Subcategories

This category has the following 4 subcategories, out of 4 total.

## Pages in category "Symmetric Difference"

The following 25 pages are in this category, out of 25 total.

### C

### S

- Set Difference as Symmetric Difference with Intersection
- Set System Closed under Symmetric Difference is Abelian Group
- Symmetric Difference is Associative
- Symmetric Difference is Commutative
- Symmetric Difference is Subset of Union
- Symmetric Difference is Subset of Union of Symmetric Differences
- Symmetric Difference of Complements
- Symmetric Difference of Equal Sets
- Symmetric Difference of Unions
- Symmetric Difference of Unions is Subset of Union of Symmetric Differences
- Symmetric Difference on Power Set forms Abelian Group
- Symmetric Difference with Complement
- Symmetric Difference with Empty Set
- Symmetric Difference with Intersection forms Boolean Ring
- Symmetric Difference with Intersection forms Ring
- Symmetric Difference with Self is Empty Set
- Symmetric Difference with Union does not form Ring
- Symmetric Difference with Universe