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:

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 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.

Chapters: 1
Corollaries: 2
Definitions: 3 4 5 6
Proofs: 7 8
Propositions: 9 10
Theorems: 11

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### References

#### Bibliography

1. Reinhardt F., Soeder H.: "dtv-Atlas zur Mathematik", Deutsche Taschenbuch Verlag, 1994, 10th Edition
2. Kohar, Richard: "Basic Discrete Mathematics, Logic, Set Theory & Probability", World Scientific, 2016