# Category:Relative Complement

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This category contains results about **relative complements**.

Let $S$ be a set, and let $T \subseteq S$, that is: let $T$ be a subset of $S$.

Then the set difference $S \setminus T$ can be written $\relcomp S T$, and is called the **relative complement of $T$ in $S$**, or the **complement of $T$ relative to $S$**.

Thus:

- $\relcomp S T = \set {x \in S : x \notin T}$

## Also see

## Subcategories

This category has the following 7 subcategories, out of 7 total.

### D

### E

### K

## Pages in category "Relative Complement"

The following 32 pages are in this category, out of 32 total.

### C

- Complement of Clopen Set is Clopen
- Complement of Direct Image Mapping of Injection equals Direct Image of Complement
- Complement of Preimage equals Preimage of Complement
- Complement of Primitive Recursive Set
- Complement of Reflexive Relation
- Complement of Relative Complement is Union with Complement
- Complement of Symmetric Relation
- Complement Relative to Subset is Subset of Complement Relative to Superset
- Complements of Components of Two-Component Partition form Partition

### I

### R

- Relative Complement inverts Subsets
- Relative Complement Mapping on Powerset is Bijection
- Relative Complement of Cartesian Product
- Relative Complement of Decreasing Sequence of Sets is Increasing
- Relative Complement of Empty Set
- Relative Complement of Relative Complement
- Relative Complement with Self is Empty Set