# SetAlgebra Implementations ## Topics ### Initializers [`init()`](/documentation/Swift/Set/init()) Creates an empty set. [`init(Source)`](/documentation/Swift/Set/init(_:)) Creates a new set from a finite sequence of items. [`init(S)`](/documentation/Swift/Set/init(_:)-9cgks) Creates a new set from a finite sequence of items. [`init(arrayLiteral: Self.Element...)`](/documentation/Swift/Set/init(arrayLiteral:)-85a3x) Creates a set containing the elements of the given array literal. ### Instance Methods [`func contains(Element) -> Bool`](/documentation/Swift/Set/contains(_:)) Returns a Boolean value that indicates whether the given element exists in the set. [`func formIntersection(S)`](/documentation/Swift/Set/formIntersection(_:)) Removes the elements of the set that aren’t also in the given sequence. [`func formSymmetricDifference(Set)`](/documentation/Swift/Set/formSymmetricDifference(_:)-22p0m) Removes the elements of the set that are also in the given sequence and adds the members of the sequence that are not already in the set. [`func formUnion(S)`](/documentation/Swift/Set/formUnion(_:)) Inserts the elements of the given sequence into the set. [`func insert(Element) -> (inserted: Bool, memberAfterInsert: Element)`](/documentation/Swift/Set/insert(_:)-nads) Inserts the given element in the set if it is not already present. [`func intersection(Set) -> Set`](/documentation/Swift/Set/intersection(_:)-1zh8f) Returns a new set with the elements that are common to both this set and the given sequence. [`func isDisjoint(with: Set) -> Bool`](/documentation/Swift/Set/isDisjoint(with:)-8ngmk) Returns a Boolean value that indicates whether this set has no members in common with the given set. [`func isSubset(of: Set) -> Bool`](/documentation/Swift/Set/isSubset(of:)-1d7pp) Returns a Boolean value that indicates whether this set is a subset of the given set. [`func isSuperset(of: Set) -> Bool`](/documentation/Swift/Set/isSuperset(of:)-9iz62) Returns a Boolean value that indicates whether this set is a superset of the given set. [`func remove(Element) -> Element?`](/documentation/Swift/Set/remove(_:)-8p2tv) Removes the specified element from the set. [`func subtract(Self)`](/documentation/Swift/Set/subtract(_:)-7uaak) Removes the elements of the given set from this set. [`func subtract(Set)`](/documentation/Swift/Set/subtract(_:)-8gc48) Removes the elements of the given set from this set. [`func subtracting(Set) -> Set`](/documentation/Swift/Set/subtracting(_:)-3n4lc) Returns a new set containing the elements of this set that do not occur in the given set. [`func symmetricDifference(S) -> Set`](/documentation/Swift/Set/symmetricDifference(_:)) Returns a new set with the elements that are either in this set or in the given sequence, but not in both. [`func union(S) -> Set`](/documentation/Swift/Set/union(_:)) Returns a new set with the elements of both this set and the given sequence. [`func update(with: Element) -> Element?`](/documentation/Swift/Set/update(with:)-2n6tk) Inserts the given element into the set unconditionally. --- Copyright © 2026 Apple Inc. All rights reserved. | [Terms of Use](https://www.apple.com/legal/internet-services/terms/site.html) | [Privacy Policy](https://www.apple.com/privacy/privacy-policy)