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2. Venn diagram - Wikipedia

   en.wikipedia.org/wiki/Venn_diagram

   v. t. e. 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 (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 ...

4. Intersection (set theory) - Wikipedia

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

   The intersection of A and B is the set A ∩ B of elements that lie in both set A and set B . Symbolic statement. A ∩ B = {x: x ∈ A and x ∈ B} In set theory, the intersection of two sets and denoted by 1 is the set containing all elements of that also belong to or equivalently, all elements of that also belong to 2.

5. Algebra of sets - Wikipedia

   en.wikipedia.org/wiki/Algebra_of_sets

   Fundamentals. 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. 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. The modern study of set theory was ...

7. Euler diagram - Wikipedia

   en.wikipedia.org/wiki/Euler_diagram

   Euler diagram. An Euler diagram (/ ˈɔɪlər /, OY-lər) is a diagrammatic means of representing sets and their relationships. They are particularly useful for explaining complex hierarchies and overlapping definitions. They are similar to another set diagramming technique, Venn diagrams.

8. Simple theorems in the algebra of sets - Wikipedia

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

   Simple theorems in the algebra of sets. 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 ...

9. De Morgan's laws - Wikipedia

   en.wikipedia.org/wiki/De_Morgan's_laws

   Consider a set of documents containing the words "cats" and "dogs". De Morgan's laws hold that these two searches will return the same set of documents: Search A: NOT (cats OR dogs) Search B: (NOT cats) AND (NOT dogs) The corpus of documents containing "cats" or "dogs" can be represented by four documents: Document 1: Contains only the word "cats".