setsymdiff: Symmetric Difference of Two Sets
In set6: R6 Mathematical Sets Interface

Description Usage Arguments Details Value See Also Examples

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

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setsymdiff(x, y, simplify = TRUE)

x %-% y

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

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,

{z : (z ε X or z ε Y) and !(z ε X and z ε Y)}

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.

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

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

# 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)