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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. List of set identities and relations - Wikipedia

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

   Three sets involved. [edit] In the left hand sides of the following identities, L{\displaystyle L}is the L eft most set, M{\displaystyle M}is the M iddle set, and R{\displaystyle R}is the R ight most set. Precedence rules. There is no universal agreement on the order of precedenceof the basic set operators.

4. 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".

5. UpSet plot - Wikipedia

   en.wikipedia.org/wiki/UpSet_plot

   UpSet plots are a data visualization method for showing set data with more than three intersecting sets. UpSet shows intersections in a matrix, with the rows of the matrix corresponding to the sets, and the columns to the intersections between these sets (or vice versa). The size of the sets and of the intersections are shown as bar charts.

6. Intersection (set theory) - Wikipedia

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

   Set theory. Statement. 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.

7. Russell's paradox - Wikipedia

   en.wikipedia.org/wiki/Russell's_paradox

   In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox published by the British philosopher and mathematician Bertrand Russell in 1901. [1][2] Russell's paradox shows that every set theory that contains an unrestricted comprehension principle leads to contradictions. [3]

8. Symmetric difference - Wikipedia

   en.wikipedia.org/wiki/Symmetric_difference

   Statement. The symmetric difference is the set of elements that are in either set, but not in the intersection. Symbolic statement. A Δ B = ( A ∖ B ) ∪ ( B ∖ A ) {\displaystyle A\,\Delta \,B=\left (A\setminus B\right)\cup \left (B\setminus A\right)} In mathematics, the symmetric difference of two sets, also known as the disjunctive union ...

9. 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.