Diszjunkt

Diszjunkt (disjoint) is a term used in mathematics, probability and related fields to denote a lack of overlap between objects. In set theory, two sets A and B are disjoint when their intersection is empty: A ∩ B = ∅. A collection {A_i} is called pairwise disjoint if A_i ∩ A_j = ∅ for i ≠ j. Disjointness is a basic assumption in many constructions, such as partitions, where a universe is partitioned into disjoint subsets whose union is the whole set.

In probability and statistics, disjoint (or mutually exclusive) events cannot occur at the same time. If A and B are disjoint, then P(A ∪ B) = P(A) + P(B). More generally, the events of a finite or countable partition are pairwise disjoint.

In combinatorics and computer science, the disjoint union refers to a construction that combines sets while preserving their identities, typically represented as A ⊔ B or as A × {0} ∪ B × {1}. In graph theory, one may speak of vertex-disjoint subgraphs or edge-disjoint paths, meaning that they share no vertices or no edges, respectively.

Examples: The sets {1,2} and {3,4} are disjoint. The events “rolling an even number” and “rolling a 1” on a fair die are disjoint.

Etymology: diszjunkt is borrowed from Latin disjunctus via other European languages and is used in Hungarian mathematical terminology.

See also: disjoint sets, mutually exclusive, disjoint union, partition, coproduct.