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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 ...
Set packing is a classical NP-complete problem in computational complexity theory and combinatorics, and was one of Karp's 21 NP-complete problems. Suppose one has a finite set S and a list of subsets of S. Then, the set packing problem asks if some k subsets in the list are pairwise disjoint (in other words, no two of them share an element).
In category theory the disjoint union is defined as a coproduct in the category of sets. As such, the disjoint union is defined up to an isomorphism, and the above definition is just one realization of the coproduct, among others. When the sets are pairwise disjoint, the usual union is another realization of the coproduct.
The set of those translates partitions the circle into a countable collection of pairwise disjoint sets, which are all pairwise congruent. Since X is not measurable for any rotation-invariant countably additive finite measure on S , finding an algorithm to form a set from selecting a point in each orbit requires that one add the axiom of choice ...
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
A partition of a set S is a set of non-empty, pairwise disjoint subsets of S, called "parts" or "blocks", whose union is all of S.Consider a finite set that is linearly ordered, or (equivalently, for purposes of this definition) arranged in a cyclic order like the vertices of a regular n-gon.
In combinatorics, a laminar set family is a set family in which each pair of sets are either disjoint or related by containment. [1] [2] Formally, a set family {S 1, S 2, ...} is called laminar if for every i, j, the intersection of S i and S j is either empty, or equals S i, or equals S j. Let E be a ground-set of elements.
Then consider ,, …, to be a maximal collection of pairwise disjoint sets (that is, is the empty set unless =, and every set in intersects with some ). Because we assumed that W {\displaystyle W} had no sunflower of size r {\displaystyle r} , and a collection of pairwise disjoint sets is a sunflower, t < r {\displaystyle t<r} .