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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.
Venn diagram of = . The symmetric difference is equivalent to the union of both relative complements, that is: [1] = (), The symmetric difference can also be expressed using the XOR operation ⊕ on the predicates describing the two sets in set-builder notation:
Comparison of skyscrapers. Comparison diagram or comparative diagram is a general type of diagram, in which a comparison is made between two or more objects, phenomena or groups of data. [1] A comparison diagram or can offer qualitative and/or quantitative information. This type of diagram can also be called comparison chart or comparison chart.
For example, comparing attributes/skills (e.g., communication, analytical, IT skills) learnt across different university degrees (e.g., mathematics, economics, psychology) Venn diagram: Venn diagram: all possible logical relations between a finite collection of different sets.
Venn diagram of . Exclusive or, exclusive disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional.
Inclusion–exclusion illustrated by a Venn diagram for three sets. Generalizing the results of these examples gives the principle of inclusion–exclusion. To find the cardinality of the union of n sets: Include the cardinalities of the sets. Exclude the cardinalities of the pairwise intersections.
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.
R-diagrams can be used to easily simplify complicated logical expressions, using a step-by-step process. Using order of operations, logical operators are applied to R-diagrams in the proper sequence. Finally, the result is an R-diagram that can be converted back into a simpler logical expression. For example, take the following expression: