# Definition:Complement

## Disambiguation

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**Complement** may refer to:

- Geometry:
- Complementary angles: two angles whose measures add up to the measure of a right angle.
- Complements of Parallelograms: The extra bits that need to be added to a pair of parallelograms sharing a line for their diagonals that need to be added to make one big parallelogram.

- Relation Theory:
- Complement of Relation: for a relation $\mathcal R$, its
**complement**is all those pairs which are not in $\mathcal R$.

- Complement of Relation: for a relation $\mathcal R$, its

- Set Theory:
- Set Complement or Relative Complement: two related concepts: all the elements of a set which are not in a given subset.

- Logic:
- Logical Complement: In logic, the negation of a statement.

- Lattice Theory:
- Complement of Lattice Element: An in a strong and precise sense incomparable element of an element of a bounded lattice.

- Graph Theory:
- Complement of Graph: a graph with the same vertex set but whose edge set is all those edges not in that graph.

## Linguistic Note

The word **complement** comes from the idea of **complete-ment**, it being the thing needed to **complete** something else.

It is a common mistake to confuse the words **complement** and **compliment**. Usually the latter is mistakenly used when the former is meant.