Returns the intersection of two objects inheriting from class Set.
setintersect(x, y) # S3 method for Interval setintersect(x, y) # S3 method for ConditionalSet setintersect(x, y) # S3 method for UnionSet setintersect(x, y) # S3 method for ComplementSet setintersect(x, y) # S3 method for ProductSet setintersect(x, y) # S3 method for Set &(x, y)
| x, y | Set |
|---|
A Set consisting of elements in both x and y.
The intersection of two sets, \(X, Y\), is defined as the set of elements that exist in both sets, $$X \cap Y = \{z : z \epsilon X \quad and \quad z \epsilon Y\}$$ In the case where no elements are common to either set, then the empty set is returned.
The intersection of two ConditionalSets is defined by combining their defining functions by an
'and', &, operator. See examples.
The intersection of fuzzy and crisp sets first coerces fuzzy sets to crisp sets by finding their support.
Other operators:
powerset(),
setcomplement(),
setpower(),
setproduct(),
setsymdiff(),
setunion()
# intersection of two sets Set$new(-2:4) & Set$new(2:5) #> {2, 3, 4} setintersect(Set$new(1, 4, "a"), Set$new("a", 6)) #> {a} Set$new(1:4) & Set$new(5:7) #> ∅ # intersection of two intervals Interval$new(1, 10) & Interval$new(5, 15) #> [5,10] Interval$new(1, 2) & Interval$new(2, 3) #> {2,...,2} Interval$new(1, 5, class = "integer") & Interval$new(2, 7, class = "integer") #> {2, 3, 4, 5} # intersection of mixed set types Set$new(1:10) & Interval$new(5, 15) #> {10, 5,...,8, 9} Set$new(5, 7) & Tuple$new(6, 8, 7) #> {7} # Ignores membership of FuzzySet FuzzySet$new(1, 0.1, 2, 0.5) & Set$new(2:5) #> {2} # intersection of conditional sets ConditionalSet$new(function(x, y) x >= y) & ConditionalSet$new(function(x, y) x == y) #> {x ∈ 𝕍, y ∈ 𝕍 : x >= y & x == y} ConditionalSet$new(function(x) x == 2) & ConditionalSet$new(function(y) y == 3) #> {x ∈ 𝕍, y ∈ 𝕍 : x == 2 & y == 3} # But be careful not to make an empty set ConditionalSet$new(function(x) x == 2) & ConditionalSet$new(function(x) x == 3) #> {x ∈ 𝕍 : x == 2 & x == 3}