# Category:Set Complement

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This category contains results about set complements.

Definitions specific to this category can be found in Definitions/Set Complement.

The **set complement** (or, when the context is established, just **complement**) of a set $S$ in a universe $\mathbb U$ is defined as:

- $\map \complement S = \relcomp {\mathbb U} S = \mathbb U \setminus S$

See the definition of Relative Complement for the definition of $\relcomp {\mathbb U} S$.

## Also see

## Subcategories

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

### D

### E

### S

## Pages in category "Set Complement"

The following 33 pages are in this category, out of 33 total.

### C

### I

- Intersection Complement of Set with Itself is Complement
- Intersection is Empty and Union is Universe if Sets are Complementary
- Intersection is Subset of Union of Intersections with Complements
- Intersection of Unions with Complements is Subset of Union
- Intersection with Complement
- Intersection with Complement is Empty iff Subset

### K

### P

### S

- Set Complement inverts Subsets
- Set Difference as Intersection with Complement
- Set Difference of Complements
- Set Intersection expressed as Intersection Complement
- Set Union expressed as Intersection Complement
- Set with Complement forms Partition
- Symmetric Difference of Complements
- Symmetric Difference with Complement
- Symmetric Difference with Universe