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 universal set $\mathbb U$ 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 5 subcategories, out of 5 total.
D
R
S
Pages in category "Set Complement"
The following 33 pages are in this category, out of 33 total.
C
- Cartesian Product with Complement
- Closure of Union and Complement imply Closure of Set Difference
- Complement of Complement
- Complement of Empty Set is Universal Set
- Complement of Universal Set is Empty Set
- Complement Union with Superset is Universe
- Complement Union with Superset is Universe/Corollary
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 Universal Set