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A set collection type is an unindexed, unordered collection that contains no duplicates, and implements set theoretic operations such as union, intersection, difference, symmetric difference, and subset testing. There are two types of sets: set and frozenset, the only difference being that set is mutable and frozenset is immutable. Elements in ...
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. [ 1 ] It is one of the fundamental operations through which sets can be combined and related to each other. A nullary union refers to a union of zero ( ) sets and it is by definition equal to the empty set.
Set theory. Statement. The intersection of A and B is the set A ∩ B of elements that lie in both set A and set B . Symbolic statement. A ∩ B = {x: x ∈ A and x ∈ B} In set theory, the intersection of two sets and denoted by 1 is the set containing all elements of that also belong to or equivalently, all elements of that also belong to 2.
Three sets involved. [edit] In the left hand sides of the following identities, L{\displaystyle L}is the L eft most set, M{\displaystyle M}is the M iddle set, and R{\displaystyle R}is the R ight most set. Precedence rules. There is no universal agreement on the order of precedenceof the basic set operators.
If D is a difference set, and g in G, then g D = {gd: d in D} is also a difference set, and is called a translate of D. The set of all translates of a difference set D forms a symmetric BIBD. In such a design there are v elements and v blocks. Each block of the design consists of k points, each point is contained in k blocks. Any two blocks ...
the set difference A \ B (also written A − B) is the set of all things that belong to A but not B. Especially when B is a subset of A, it is also called the relative complement of B in A. With B c as the absolute complement of B (in the universal set U), A \ B = A ∩ B c. their symmetric difference A Δ B is the set of all things that belong ...
De Morgan's laws commonly apply to text searching using Boolean operators AND, OR, and NOT. Consider a set of documents containing the words "cats" and "dogs". De Morgan's laws hold that these two searches will return the same set of documents: Search A: NOT (cats OR dogs) Search B: (NOT cats) AND (NOT dogs)
Symmetric difference of sets A and B, denoted A B or A ⊖ B, is the set of all objects that are a member of exactly one of A and B (elements which are in one of the sets, but not in both). For instance, for the sets {1, 2, 3} and {2, 3, 4}, the symmetric difference set is {1, 4}.