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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. 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".

4. Intersection (set theory) - Wikipedia

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

   Intersections of the unaccented modern Greek, Latin, and Cyrillic scripts, considering only the shapes of the letters and ignoring their pronunciation Example of an intersection with sets The intersection of two sets A {\displaystyle A} and B , {\displaystyle B,} denoted by A ∩ B {\displaystyle A\cap B} , [ 3 ] is the set of all objects that ...

5. List of set identities and relations - Wikipedia

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

   To investigate the left distributivity of set subtraction over unions or intersections, consider how the sets involved in (both of) De Morgan's laws are all related: () = = () always holds (the equalities on the left and right are De Morgan's laws) but equality is not guaranteed in general (that is, the containment might be strict).

6. Simple theorems in the algebra of sets - Wikipedia

   en.wikipedia.org/wiki/Simple_theorems_in_the...

   The simple theorems in the algebra of sets are some of the elementary properties of the algebra of union (infix operator: ∪), intersection (infix operator: ∩), and set complement (postfix ') of sets. These properties assume the existence of at least two sets: a given universal set, denoted U, and the empty set, denoted {}.

7. Venn diagram - Wikipedia

   en.wikipedia.org/wiki/Venn_diagram

   The combined region of the two sets is called their union, denoted by A ∪ B, where A is the orange circle and B the blue. The union in this case contains all living creatures that either are two-legged or can fly (or both). The region included in both A and B, where the two sets overlap, is called the intersection of A and B, denoted by A ∩ B.

8. Ring of sets - Wikipedia

   en.wikipedia.org/wiki/Ring_of_sets

   The open sets and closed sets of any topological space are closed under both unions and intersections. [ 1 ] On the real line R , the family of sets consisting of the empty set and all finite unions of half-open intervals of the form ( a , b ] , with a , b ∈ R is a ring in the measure-theoretic sense.

9. Family of sets - Wikipedia

   en.wikipedia.org/wiki/Family_of_sets

   A topological space consists of a pair (,) where is a set (whose elements are called points) and is a topology on , which is a family of sets (whose elements are called open sets) over that contains both the empty set and itself, and is closed under arbitrary set unions and finite set intersections.