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When dealing with particular situations in mathematics, it is often easier to have a set which contains all the elements we deal with. This set is called a universal set and we want to define it properly.

Definition: Universal Set

A universal set $U$ is a set of elements fulfilling all the necessary or sufficient properties that we deal with in a particular situation.

In a Venn diagram, we draw the universal set as a frame in which we place the sets of our consideration (here a set $A$).


  1. If you are considering all vans, the universal set could be the set of all cars.
  2. The set of all possibilities to win in a coupon-based lottery could be considered as the universal set of all the possibilities printed on the coupons produced for this lottery.
  3. The set of all possible words which can be constructed from Latin letters is the universal set of all words which have a meaning in the Englisch language.

| | | | | Contributors: bookofproofs | References: [979], [7838]

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Bibliography (further reading)

[7838] Kohar, Richard: “Basic Discrete Mathematics, Logic, Set Theory & Probability”, World Scientific, 2016

[979] Reinhardt F., Soeder H.: “dtv-Atlas zur Mathematik”, Deutsche Taschenbuch Verlag, 1994, 10

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