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A simple Carroll diagram. A Carroll diagram, Lewis Carroll's square, biliteral diagram or a two-way table is a diagram used for grouping things in a yes/no fashion. Numbers or objects are either categorised as 'x' (having an attribute x) or 'not x' (not having an attribute 'x').
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.
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 ...
De Morgan's laws represented with Venn diagrams.In each case, the resultant set is the set of all points in any shade of blue. In propositional logic and Boolean algebra, De Morgan's laws, [1] [2] [3] also known as De Morgan's theorem, [4] are a pair of transformation rules that are both valid rules of inference.
The 2x2 matrices show the same information like the Venn diagrams. (This matrix is similar to this Hasse diagram.) In set theory the Venn diagrams represent the set, which is marked in red. These 15 relations, except the empty one, are minterms and can be the case. The relations in the files below are disjunctions.
Square of opposition. The lower case letters (a, e, i, o) are used instead of the upper case letters (A, E, I, O) here in order to be visually distinguished from the surrounding upper case letters S (Subject term) and P (Predicate term). In the Venn diagrams, black areas are empty and red areas are nonempty. White areas may or may not be empty.
A diagram representing a two-state Markov chain. The states are represented by 'A' and 'E'. The numbers are the probability of flipping the state. Discrete mathematics, broadly speaking, is the study of individual, countable mathematical objects. An example is the set of all integers. [42]
Venn diagrams are a more restrictive form of Euler diagrams. A Venn diagram must contain all 2 n logically possible zones of overlap between its n curves, representing all combinations of inclusion/exclusion of its constituent sets. Regions not part of the set are indicated by coloring them black, in contrast to Euler diagrams, where membership ...