setcomplement: Complement of Two Sets

In set6: R6 Mathematical Sets Interface

Description

Returns the set difference of two objects inheriting from class Set. If y is missing then the complement of x from its universe is returned.

Usage

setcomplement(x, y, simplify = TRUE)

## S3 method for class 'Set'
setcomplement(x, y, simplify = TRUE)

## S3 method for class 'Interval'
setcomplement(x, y, simplify = TRUE)

## S3 method for class 'FuzzySet'
setcomplement(x, y, simplify = TRUE)

## S3 method for class 'ConditionalSet'
setcomplement(x, y, simplify = TRUE)

## S3 method for class 'Reals'
setcomplement(x, y, simplify = TRUE)

## S3 method for class 'Rationals'
setcomplement(x, y, simplify = TRUE)

## S3 method for class 'Integers'
setcomplement(x, y, simplify = TRUE)

## S3 method for class 'ComplementSet'
setcomplement(x, y, simplify = TRUE)

## S3 method for class 'Set'
x - y

Arguments

x, y	Set
simplify	logical, if TRUE (default) returns the result in its simplest form, usually a Set or UnionSet, otherwise a ComplementSet.

Details

The difference of two sets, X, Y, is defined as the set of elements that exist in set X and not Y,

X-Y = {z : z ε X and !(z ε Y)}

The set difference of two ConditionalSets is defined by combining their defining functions by a negated 'and', !&, operator. See examples.

The complement of fuzzy and crisp sets first coerces fuzzy sets to crisp sets by finding their support.

Value

An object inheriting from Set containing the set difference of elements in x and y.

See Also

Other operators: powerset(), setintersect(), setpower(), setproduct(), setsymdiff(), setunion()

Examples

# absolute complement
setcomplement(Set$new(1, 2, 3, universe = Reals$new()))
setcomplement(Set$new(1, 2, universe = Set$new(1, 2, 3, 4, 5)))

# complement of two sets

Set$new(-2:4) - Set$new(2:5)
setcomplement(Set$new(1, 4, "a"), Set$new("a", 6))

# complement of two intervals

Interval$new(1, 10) - Interval$new(5, 15)
Interval$new(1, 10) - Interval$new(-15, 15)
Interval$new(1, 10) - Interval$new(-1, 2)

# complement of mixed set types

Set$new(1:10) - Interval$new(5, 15)
Set$new(5, 7) - Tuple$new(6, 8, 7)

# FuzzySet-Set returns a FuzzySet
FuzzySet$new(1, 0.1, 2, 0.5) - Set$new(2:5)
# Set-FuzzySet returns a Set
Set$new(2:5) - FuzzySet$new(1, 0.1, 2, 0.5)

# complement of conditional sets

ConditionalSet$new(function(x, y, simplify = TRUE) x >= y) -
  ConditionalSet$new(function(x, y, simplify = TRUE) x == y)

# complement of special sets
Reals$new() - NegReals$new()
Rationals$new() - PosRationals$new()
Integers$new() - PosIntegers$new()

set6 documentation built on Oct. 18, 2021, 5:06 p.m.