set6 (version 0.2.3)

setsymdiff: Symmetric Difference of Two Sets

Description

Returns the symmetric difference of two objects inheriting from class Set.

Usage

setsymdiff(x, y, simplify = TRUE)
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.

Value

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

Details

The symmetric difference, aka disjunctive union, of two sets, $X,Y$, is defined as the set of elements that exist in set $X$ or in $Y$ but not both, $$\begin{gathered} \{z:(zϵX\cup zϵY) \\ \cap \\ \mathrm{\neg }(zϵX\cap zϵY)\} \end{gathered}$$

The symmetric difference can also be expressed as the union of two sets minus the intersection. Therefore setsymdiff is written as a thin wrapper over these operations, so for two sets, A,B: A %-% B = (A | B) - (A & B).

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

See Also

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

Examples

# NOT RUN {
# symmetrical difference compared to union and intersection
Set$new(1, 2, 3) %-% Set$new(3, 4)
(Set$new(1, 2, 3) | Set$new(3, 4)) - (Set$new(1, 2, 3) & Set$new(3, 4))

# ConditionalSets demonstrate the internal logic
ConditionalSet$new(function(x) x > 0) %-%
  ConditionalSet$new(function(y) y == 0)
# }