venn diagrams and the logic of class
sources:
https://en.wikipedia.org/wiki/Venn_diagram
https://en.wikipedia.org/wiki/Logic_of_class
https://www.lucidchart.com/pages/tutorial/venn-diagram
What is a Venn diagram?
A Venn diagram uses overlapping circles or other shapes to illustrate
the logical relationships between two or more sets of items. Often, they
serve to graphically organize things, highlighting how the items are
similar and different.
Venn diagrams, also called Set diagrams or Logic diagrams, are widely
used in mathematics, statistics, logic, teaching, linguistics, computer
science and business. Many people first encounter them in school as they
study math or logic, since Venn diagrams became part of “new math”
curricula in the 1960s. These may be simple diagrams involving two or
three sets of a few elements, or they may become quite sophisticated,
including 3D presentations, as they progress to six or seven sets and
beyond. They are used to think through and depict how items relate to
each within a particular “universe” or segment. Venn diagrams allow
users to visualize data in clear, powerful ways, and therefore are
commonly used in presentations and reports. They are closely related to
Euler diagrams, which differ by omitting sets if no items exist in them.
Venn diagrams show relationships even if a set is empty.
Venn diagram: wiki
A Venn diagram may also be called a primary diagram, set diagram or
logic diagram. It is a diagram that shows all possible logical relations
between a finite collection of different sets. These diagrams depict
elements as points in the plane, and sets as regions inside closed
curves. A Venn diagram consists of multiple overlapping closed curves,
usually circles, each representing a set. The points inside a curve
labelled S represent elements of the set S, while points outside the
boundary represent elements not in the set S. This lends itself to
intuitive visualizations; for example, the set of all elements that are
members of both sets S and T, denoted S ∩ T and read "the intersection
of S and T", is represented visually by the area of overlap of the
regions S and T.[1][2]
In Venn diagrams, the curves are overlapped in every possible way,
showing all possible relations between the sets. They are thus a special
case of Euler diagrams, which do not necessarily show all relations.
Venn diagrams were conceived around 1880 by John Venn. They are used to
teach elementary set theory, as well as illustrate simple set
relationships in probability, logic, statistics, linguistics, and
computer science.
A Venn diagram in which the area of each shape is proportional to the
number of elements it contains is called an area-proportional (or
scaled) Venn diagram.
logic of class: WIKI
Venn diagrams are used heavily in the logic of class branch of reasoning.
The logic of class is a branch of logic that distinguishes valid from
invalid syllogistic reasonings by the use of Venn Diagrams.[1]
In syllogistic reasoning each premise takes one of the following forms, referring to an individual or class of individuals.
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