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  2. Union (set theory) - Wikipedia

    en.wikipedia.org/wiki/Union_(set_theory)

    For example, the union of three sets A, B, and C contains all elements of A, all elements of B, and all elements of C, and nothing else. Thus, x is an element of A ∪ B ∪ C if and only if x is in at least one of A, B, and C. A finite union is the union of a finite number of sets; the phrase does not imply that the union set is a finite set ...

  3. Union-closed sets conjecture - Wikipedia

    en.wikipedia.org/wiki/Union-closed_sets_conjecture

    The union-closed sets conjecture, also known as Frankl’s conjecture, is an open problem in combinatorics posed by Péter Frankl in 1979. A family of sets is said to be union-closed if the union of any two sets from the family belongs to the family.

  4. Inclusion–exclusion principle - Wikipedia

    en.wikipedia.org/wiki/Inclusion–exclusion...

    The first occurrence of the problem of counting the number of derangements is in an early book on games of chance: Essai d'analyse sur les jeux de hazard by P. R. de Montmort (1678 – 1719) and was known as either "Montmort's problem" or by the name he gave it, "problème des rencontres." [10] The problem is also known as the hatcheck problem.

  5. Algebra of sets - Wikipedia

    en.wikipedia.org/wiki/Algebra_of_sets

    The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".

  6. List of set identities and relations - Wikipedia

    en.wikipedia.org/wiki/List_of_set_identities_and...

    In constructive mathematics, "not empty" and "inhabited" are not equivalent: every inhabited set is not empty but the converse is not always guaranteed; that is, in constructive mathematics, a set that is not empty (where by definition, "is empty" means that the statement () is true) might not have an inhabitant (which is an such that ).

  7. Set theory - Wikipedia

    en.wikipedia.org/wiki/Set_theory

    Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects.Although objects of any kind can be collected into a set, set theory – as a branch of mathematics – is mostly concerned with those that are relevant to mathematics as a whole.

  8. Boole's inequality - Wikipedia

    en.wikipedia.org/wiki/Boole's_inequality

    We can use Boole's Inequality to solve this problem. By finding the complement of event "all five are good", we can change this question into another condition: P( at least one estimation is bad) = 0.05 ≤ P( A 1 is bad) + P( A 2 is bad) + P( A 3 is bad) + P( A 4 is bad) + P( A 5 is bad) One way is to make each of them equal to 0.05/5 = 0.01 ...

  9. Disjoint union - Wikipedia

    en.wikipedia.org/wiki/Disjoint_union

    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.

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