R: Union of Sets

setunion {set6} | R Documentation

## Union of Sets

### Description

Returns the union of objects inheriting from class Set.

### Usage

    setunion(..., simplify = TRUE)

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

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

### Arguments

`...` | Sets
`simplify` | logical, if `TRUE` (default) returns the result in its simplest (unwrapped) form, usually a `Set`, otherwise a `UnionSet`.
`x, y` | Set

### Details

The union of N sets, X1, ..., XN, is defined as the set of elements that exist in one or more sets,

U = {x : x ε X1 or x ε X2 or ... or x ε XN}

The union of multiple ConditionalSets is given by combining their defining functions by an 'or', `|`, operator. See examples.

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

### Value

An object inheriting from Set containing the union of supplied sets.

### See Also

Other operators: `powerset()`, `setcomplement()`, `setintersect()`, `setpower()`, `setproduct()`, `setsymdiff()`

### Examples

    # union of Sets

    Set$new(-2:4) + Set$new(2:5)
    setunion(Set$new(1, 4, "a"), Set$new("a", 6))
    Set$new(1, 2) + Set$new("a", 1i) + Set$new(9)

    # union of intervals

    Interval$new(1, 10) + Interval$new(5, 15) + Interval$new(20, 30)
    Interval$new(1, 2, type = "()") + Interval$new(2, 3, type = "(]")
    Interval$new(1, 5, class = "integer") +
      Interval$new(2, 7, class = "integer")

    # union of mixed types

    Set$new(1:10) + Interval$new(5, 15)
    Set$new(1:10) + Interval$new(5, 15, class = "integer")
    Set$new(5, 7) | Tuple$new(6, 8, 7)

    # union of FuzzySet
    FuzzySet$new(1, 0.1, 2, 0.5) + Set$new(2:5)

    # union of conditional sets

    ConditionalSet$new(function(x, y) x >= y) +
      ConditionalSet$new(function(x, y) x == y) +
      ConditionalSet$new(function(x) x == 2)

    # union of special sets
    PosReals$new() + NegReals$new()
    Set$new(-Inf, Inf) + Reals$new()

[Package set6 version 0.2.0 Index]