## absorption laws

Overview page. Subjects: Computing.

The two self-dual laws

*x* ∨ (*x* ∧ *y*) = *x*

*x* ∧ (*x* ∨ *y*) = *x*

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

## 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...

## 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 *x* ∈ *S*null...

## complement

Overview page. Subjects: Computing.

*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 *S¯*. Formally, *S*′ = {*x* | (*x* ∈ *null...*

## De Morgan's laws

Overview page. Subjects: Computing.

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

## 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 *A*−*B* is also used. The set is represented...

## 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.

## 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...

## 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...

## 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...

## 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 (*A* ∖ *B*) ∪ (*B* ∖ *A*). The notation *A* Δ *B* is also used. The set is represented by the...

## union

Overview page. Subjects: Mathematics.

*S* and *T*, say, usually expressed as *S* ∪ *T* ∪ is regarded as an operation on sets, the union operation,...

## 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...