Search results
Results From The WOW.Com Content Network
In computer science, a disjoint-set data structure, also called a union–find data structure or merge–find set, is a data structure that stores a collection of disjoint (non-overlapping) sets. Equivalently, it stores a partition of a set into disjoint subsets .
In mathematics, the disjoint union (or discriminated union) of the sets A and B is the set formed from the elements of A and B labelled (indexed) with the name of the set from which they come. So, an element belonging to both A and B appears twice in the disjoint union, with two different labels.
In the examples below, the Euler diagram depicts that the sets Animal and Mineral are disjoint since the corresponding curves are disjoint, and also that the set Four Legs is a subset of the set of Animals. The Venn diagram, which uses the same categories of Animal, Mineral, and Four Legs, does not encapsulate these relationships.
Two disjoint sets. In set theory in mathematics and formal logic, two sets are said to be disjoint sets if they have no element in common. Equivalently, two disjoint sets are sets whose intersection is the empty set. [1] For example, {1, 2, 3} and {4, 5, 6} are disjoint sets, while {1, 2, 3} and {3, 4, 5} are not disjoint. A collection of two ...
Intersecting and disjoint sets [ edit ] We say that A {\displaystyle A} intersects (meets) B {\displaystyle B} if there exists some x {\displaystyle x} that is an element of both A {\displaystyle A} and B , {\displaystyle B,} in which case we also say that A {\displaystyle A} intersects (meets) B {\displaystyle B} at x {\displaystyle x} .
A partition of a set X is a set of non-empty subsets of X such that every element x in X is in exactly one of these subsets [2] (i.e., the subsets are nonempty mutually disjoint sets). Equivalently, a family of sets P is a partition of X if and only if all of the following conditions hold: [3]
Disjoint union – In mathematics, operation on sets; Inclusion–exclusion principle – Counting technique in combinatorics; Intersection (set theory) – Set of elements common to all of some sets; Iterated binary operation – Repeated application of an operation to a sequence
Furthermore, denoting = and =, then and are always disjoint, so and partition. Consequently, assuming intersection and symmetric difference as primitive operations, the union of two sets can be well defined in terms of symmetric difference by the right-hand side of the equality