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A universal set, denoted as U
or E,
is a set that contains all of the elements of the related sets. This means that all the related sets are subsets of the universal set.
The exact definition of a universal set can be determined according to the context. Several examples are shown in the table.
| Set A | Set B | Universal Set U |
|---|---|---|
| { Amsterdam, Buenos Aires, Madrid, Paris, Doha } | { Berlin } | Capital cities of the world |
| { Blue, Yellow } | { Green, Purple, Black } | Colors |
| {0,1,2,3,... } | {...,-3,-2,-1 } | Integer numbers |
Note that the union of two or more sets is not always the same as the universal set. Consider the following example. U&={1,2,3,4,5,6,7,8,9} A&={1,2,3} B&={3,4,5,6} A ⋃ B&={1,2,3,4,5,6} As seen, the elements 7, 8, and 9 belong to the universal set but do not belong to A⋃ B.