Venn diagram: Difference between revisions
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==Examples== | ==Examples== | ||
Suppose X and Y are sets. Various operations allow us to build new sets from them, and these definitions are illustrated using the three Venn diagrams in the figure. | Suppose X and Y are sets. Various operations allow us to build new sets from them, and these definitions are illustrated using the three Venn diagrams in the figure.<ref name=Oakhill/> | ||
==== Union ==== | ==== Union ==== | ||
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In the presence of a universal set we can define X′, the complement of X, to be U−X. X′ it contains everything in the universe apart from the elements of X. | In the presence of a universal set we can define X′, the complement of X, to be U−X. X′ it contains everything in the universe apart from the elements of X. | ||
==References== | |||
{{Reflist|refs= | |||
<ref name=Oakhill> | |||
{{cite book |title=Thinking and reasoning |author=Alan Garnham, Jane Oakhill |url=http://books.google.com/books?id=f1Mz44k3B18C&pg=PA105 |pages=pp. 105 ''ff'' |chapter=§6.2.3b: Venn diagrams |isbn=0631170030 |publisher=Wiley-Blackwell |year=1994}} | |||
</ref> | |||
}} | |||
Revision as of 12:24, 4 July 2011
A Venn diagram is an arrangement of intersecting circles used to visually represent logical concepts and propositions.
Examples
Suppose X and Y are sets. Various operations allow us to build new sets from them, and these definitions are illustrated using the three Venn diagrams in the figure.[1]
Union
The union of X and Y, written X∪Y, contains all the elements in X and all those in Y.
Intersection
The intersection of X and Y, written X∩Y, contains all the elements that are common to both X and Y.
Set difference
The difference X minus Y, written X−Y or X\Y, contains all those elements in X that are not also in Y.
Complement and universal set
The universal set (if it exists), usually denoted U, is a set of which everything under discussion is a member. In pure set theory, normally sets are the only objects considered. In that case, U would be the set of all sets. However, one may also consider sets that are collections of numbers, or colors, or books, for example; see Set (mathematics).
In the presence of a universal set we can define X′, the complement of X, to be U−X. X′ it contains everything in the universe apart from the elements of X.
References
- ↑ Alan Garnham, Jane Oakhill (1994). “§6.2.3b: Venn diagrams”, Thinking and reasoning. Wiley-Blackwell, pp. 105 ff. ISBN 0631170030.