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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.
An information diagram is a type of Venn diagram used in information theory to illustrate relationships among Shannon's basic measures of information: entropy, joint entropy, conditional entropy and mutual information. [1] [2] Information
Venn diagram for various information measures associated with correlated variables X and Y. The area contained by both circles is the joint entropy H(X,Y). The circle on the left (red and cyan) is the individual entropy H(X), with the red being the conditional entropy H(X|Y).
A naive theory in the sense of "naive set theory" is a non-formalized theory, that is, a theory that uses natural language to describe sets and operations on sets. Such theory treats sets as platonic absolute objects. The words and, or, if ... then, not, for some, for every are treated as in ordinary mathematics. As a matter of convenience, use ...
Venn diagram of (true part in red) In logic and mathematics, the logical biconditional, also known as material biconditional or equivalence or biimplication or bientailment, is the logical connective used to conjoin two statements and to form the statement "if and only if" (often abbreviated as "iff " [1]), where is known as the antecedent, and the consequent.
This construction is used in graph theory, to define the cycle space of a graph. From the property of the inverses in a Boolean group, it follows that the symmetric difference of two repeated symmetric differences is equivalent to the repeated symmetric difference of the join of the two multisets, where for each double set both can be removed.
The positive diagram of A is the set of all atomic σ'-sentences that A satisfies. It is denoted by diag + A. The elementary diagram of A is the set eldiag A of all first-order σ'-sentences that are satisfied by A or, equivalently, the complete (first-order) theory of the natural expansion of A to the signature σ'.
This result has been used as a basic building block for proving other inequalities in information theory, in particular, those known as Shannon-type inequalities. Conditional mutual information is also non-negative for continuous random variables under certain regularity conditions.