What are Universal Sets?

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bababeta | Middle School Teacher | (Level 1) Adjunct Educator

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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.

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.

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gsenviro's profile pic

gsenviro | College Teacher | (Level 1) Educator Emeritus

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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.

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balajia | College Teacher | (Level 1) eNoter

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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} ;

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