source: http://www.amathsdictionaryforkids.com/

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Math Essentials
Advanced - GRE Math Book

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Math Essentials
Advanced - GRE Math Book

source: http://www.amathsdictionaryforkids.com/

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Math Essentials
Advanced - GRE Math Book

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Math Essentials
Advanced - GRE Math Book

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Math Essentials
Advanced - GRE Math Book

source: Department of Mathematics, University of Houston by Jiwen He

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Math Essentials
Advanced - GRE Math Book

Diagrams make mathematics easier because they help us to see the whole situation at a glance. The English mathematician John Venn (1834–1923) began using diagrams to represent sets. His diagrams are now called Venn diagrams.
In most problems involving sets, it is convenient to choose a larger set that contains all of the elements in all of the sets being considered. This larger set is called the universal set, and is usually given the symbol E.
In a Venn diagram, the universal set is generally drawn as a large rectangle, and then other sets are represented by circles within this rectangle.


Venn diagrams with complements, unions and intersections

• Sets are represented in a Venn diagram by circles drawn inside a rectangle representing the universal set.
• The region outside the circle represents the complement of the set.
• The overlapping region of two circles represents the intersection of the two sets.
• Two circles together represent the union of the two sets.
• When two sets are disjoint, we can draw the two circles without any overlap.
• When one set is a subset of another, we can draw its circle inside the circle of the other set.

source: SETS AND VENN DIAGRAMS under the Creative Commons AttributionNonCommercial-NoDerivs 3.0 Unported License. 2011