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 $A$).
Examples:
 If you are considering all vans, the universal set could be the set of all cars.
 The set of all possibilities to win in a couponbased lottery could be considered as the universal set of all the possibilities printed on the coupons produced for this lottery.
 The set of all possibilities to win in a couponbased lottery could be considered as the universal set of all the possibilities printed on the coupons produced for this lottery.
Mentioned in:
Chapters: 1
Corollaries: 2
Definitions: 3 4 5 6
Proofs: 7 8
Propositions: 9 10
Theorems: 11
Thank you to the contributors under CC BYSA 4.0!
 Github:

References
Bibliography
 Reinhardt F., Soeder H.: "dtvAtlas zur Mathematik", Deutsche Taschenbuch Verlag, 1994, 10th Edition
 Kohar, Richard: "Basic Discrete Mathematics, Logic, Set Theory & Probability", World Scientific, 2016