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# complement fn (ComplementFn)

The complement of a given SetOrClass C is the SetOrClass of all things that are not instances of C. In other words, an object is an instance of the complement of a SetOrClass C just in case it is not an instance of C.

## Ontology

SUMO / SET/CLASS-THEORY

## Class(es)

 class

inheritable relation

unary function

complement fn

## Coordinate term(s)

absolute value fn  abstraction fn  arc cosine fn  arc sine fn  arc tangent fn  back fn  begin fn  begin node fn  cardinality fn  ceiling fn  cosine fn  cut set fn  denominator fn  end fn  end node fn  extension fn  floor fn  front fn  future fn  generalized intersection fn  generalized union fn  giga fn  imaginary part fn  immediate future fn  immediate past fn  initial node fn  integer square root fn  kilo fn  list length fn  magnitude fn  mega fn  micro fn  milli fn  minimal cut set fn  nano fn  numerator fn  organization fn  past fn  path weight fn  pico fn  power set fn  predecessor fn  principal host fn  probability fn  property fn  rational number fn  real number fn  reciprocal fn  round fn  signum fn  sine fn  skin fn  square root fn  successor fn  tangent fn  tera fn  terminal node fn  wealth fn  when fn  year fn

## Type restrictions

set or class ComplementFn(set or class)

## Axioms (2)

entity is an instance of "the complement of class" if and only if entity is not an instance of class.
```(<=>
(instance
?ENTITY
(ComplementFn ?CLASS))
(not
(instance ?ENTITY ?CLASS)))```

If class1 is an instance of set or class and class2 is an instance of set or class, then "the difference between class1 and class2" is equal to "the union of class1 and "the complement of class2"".
```(=>
(and
(instance ?CLASS1 SetOrClass)
(instance ?CLASS2 SetOrClass))
(equal
(RelativeComplementFn ?CLASS1 ?CLASS2)
(IntersectionFn
?CLASS1
(ComplementFn ?CLASS2))))```