# What are Universal Sets?

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A universal set does not have to be the set of everything that is known or thought to exist - such as the planets, extraterrestrial life and the galaxies - even though that would be one example of a universal set.

A **universal set** is all the elements, or members, of any group under consideration and the collection of all objects in a particular context or theory. All other sets in that framework constitute subsets of the universal set, which is denoted as an uppercase italic letter *U*. The objects themselves are known as elements or members of *U*. The precise definition of *U* depends the context or theory under consideration.

Some philosophers have attempted to define *U* as the set of all objects (including all sets, because sets are objects). This notion of *U* leads to a contradiction, because *U*, which contains everything, must therefore contain the set of all sets that are *not* members of themselves.

**Sources:**

A universal set is a set that contains all the objects or elements that are possible in a given context.

For example, while discussing prime numbers, a set containing all the prime numbers is a universal set. Similarly, the names of all the countries constitute a universal set, if the context is the names of the countries.

Sometimes, universal sets are thought to contain "everything", i.e. truly universal sets. The existence of such a set would lead to a contradiction, known as Russell's Paradox.

so, depending on the context, we can figure out what a universal set contains.

hope this helps.

**Universal Set:** If there are some sets under consideration ,then there happens to be a set which is a superset of each one of the given sets . Such a set is known as the universal set and is denoted by "`uuu` " or " `xi` " or " `mu` "

Here are the examples :

1)

P = {x/x is an even natural number} ;

Q = {x/x is an odd natural number} ;

N = {x/x is a natural number} ;

so , we can say that

N `sup` P, N `sup` Q

Here N is called the universal set.

2)

A ={1,2,3,5,7}

B ={2,4,6,8,10}

C= {7,9,10}

D= {3,4,8,9,10}

Universal set for these above sets is U = {1,2,3,4,5,6,7,8,9,10}

or U = {x/x is a natural number} ;

or U = {x/x is a whole number} ;