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2. Venn diagram - Wikipedia

   en.wikipedia.org/wiki/Venn_diagram

   A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science.

3. Set theory - Wikipedia

   en.wikipedia.org/wiki/Set_theory

   In this case, if the choice of U is clear from the context, the notation A c is sometimes used instead of U \ A, particularly if U is a universal set as in the study of Venn diagrams. Symmetric difference of sets A and B , denoted A B or A ⊖ B , is the set of all objects that are a member of exactly one of A and B (elements which are in one ...

4. 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).

5. Set (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Set_(mathematics)

   A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...

6. Universe (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Universe_(mathematics)

   The most common use of a Grothendieck universe U is to take U as a replacement for the category of all sets. One says that a set S is U-small if S ∈U, and U-large otherwise. The category U-Set of all U-small sets has as objects all U-small sets and as morphisms all functions between these sets. Both the object set and the morphism set are ...

7. Intersection (set theory) - Wikipedia

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

   Since all vacuously satisfy the required condition, the intersection of the empty collection of subsets of is all of . In formulas, ⋂ ∅ = X . {\displaystyle \bigcap \varnothing =X.} This matches the intuition that as collections of subsets become smaller, their respective intersections become larger; in the extreme case, the empty ...

8. File:Venn0111.svg - Wikipedia

   en.wikipedia.org/wiki/File:Venn0111.svg

   In set theory the Venn diagrams tell, that there is an element in one of the red intersections. (The existential quantifications for the red intersections are combined by or. They can be combined by the exclusive or as well.) Relations like subset and implication, arranged in the same kind of matrix as above. In set theory the Venn diagrams tell,

9. U - Wikipedia

   en.wikipedia.org/wiki/U

   'u' is the symbol for the atomic mass unit, and 'U' is the symbol for one enzyme unit. In the International Phonetic Alphabet, the close back rounded vowel is represented by the lowercase u . 'U' is also the source of the mathematical symbol ∪, representing a union. It is used mainly for Venn diagrams and geometry.