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universal set

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absorption laws

Overview page. Subjects: Computing.

The two self-dual laws

x ∨ (xy) = x

x ∧ (xy) = x

(see duality) that are satisfied by all elements x,y in a...

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algebra of sets

Overview page. Subjects: Mathematics.

The set of all subsets of a universal set E is closed under the binary operations∪(union) and∩(intersection) and the unary operation ′ (complementation). The following are some of the...

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characteristic function

Overview page. Subjects: Probability and Statistics — Computing.

Of a subset S of a universal set U. A function that indicates whether or not an element is a member of the subset S. It is the function f: U → {0,1} defined as follows: f(x) = 1 if xSnull...

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complement

Overview page. Subjects: Computing.

1 of a set, S, with respect to some universal set U. The set consisting of elements that are in U but not in S; it is usually denoted by S′, ~S, or . Formally, S′ = {x | (xnull...

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De Morgan's laws

Overview page. Subjects: Computing.

For all sets A and B (subsets of a universal set), (AB)′=A′∩B′ and (AB)′=A′∪B′. These are De Morgan's laws.

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difference set

Overview page. Subjects: Mathematics.

The difference A\B of sets A and B (subsets of a universal set) is the set consisting of all elements of A that are not elements of B. The notation AB is also used. The set is represented...

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intersection

Overview page. Subjects: Mathematics.

An element belongs to the intersection of two sets, A and B if and only if it belongs to both A and B. The intersection is denoted by A ⋂ B.

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set algebra

Overview page. Subjects: Computing.

The algebra that consists of the set of subsets of some universal set U together with the associated operations of union, intersection, and complement. The set of subsets associated with...

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solution

Overview page. Subjects: Mathematics.

A solution of a set of equations is an element, belonging to some appropriate universal set, specified or understood, that satisfies the equations. For a set of equations in n unknowns, a...

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solution set

Overview page. Subjects: Mathematics.

The solution set of a set of equations is the set consisting of all the solutions. It may be considered as a subset of some appropriate universal set, specified or understood. See also...

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symmetric difference

Overview page. Subjects: Mathematics.

For sets A and B (subsets of some universal set), the symmetric difference, denoted by A+B, is the set (AB) ∪ (BA). The notation A Δ B is also used. The set is represented by the...

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union

Overview page. Subjects: Mathematics.

1 of two sets. The set that results from combining the elements of two sets S and T, say, usually expressed as ST ∪ is regarded as an operation on sets, the union operation,...

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Venn diagram

Overview page. Subjects: Mathematics.

A simple diagram (see diagram) used to represent unions and intersections of sets. The diagram, described by Venn in 1880 and popularized by his 1881 book Symbolic Logic, was introduced by...

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