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what is universal set

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Answer 1

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Universal Set

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Universal set is used to build the foundation of two or more sets which are also considered as the subsets of the universal set. The universal set, denoted by U, is a set or the larger set that contains elements of all the related sets, that too without any repetition of elements. Consider two sets, A = {x,y,z} and B = {1,2,3,x,y}, then the universal set associated with these two sets is U = {1,2,3,x,y,z}.

The elements in the universal set are not repeated, thus they are unique. In this article, let's learn about the universal set, its definition, representation with solved examples.

What Is Universal Set?

The universal set is a collection of all elements or members of all the related sets, known as its subsets. All the stars in a milky way galaxy is a good example of a universal set if we consider all the stars in the milky way galaxy. When we study numbers in mathematics, we are interested in the set of natural numbers. This basic set is considered a universal set and its subsets are even numbers, prime numbers, etc.

Universal Set Definition

The universal set is the set of all elements or members of all related sets. It is usually denoted by the symbol E or U. For example, in human population studies, the universal set is the set of all the people in the world. The set of all people in each country can be considered as a subset of this universal set.

A universal set can be either a finite or infinite set.

The set of natural numbers is a typical example of an infinite universal set. Set of natural numbers: {1,2,3,...}. Here, the ellipsis mark (...) denotes that the set goes on without an end.

Symbol of Universal Set

The universal set is usually represented by the symbol E or U. It consists of all the elements of its subsets, including its own elements.

Example of Universal Set

Let's consider an example with three sets, A, B, and C. Here, A = {2, 4, 6}, B = {1, 3, 7, 9, 11}, and C = {4, 8, 11}. We need to find the universal set for all three sets A, B, and C.

All the elements of the given sets are contained in the universal set. Thus, the universal set U of A, B, and C is given by:

U = {1, 2, 3, 4, 6, 7, 8, 9, 11}

We can see that all the elements of the three sets are present in the universal set without any repetition. Thus, we can say that all the elements in the universal set are unique.

The sets A, B, and C are contained in the universal set, then these sets are also called subsets of the Universal set.

A ⊂ U (A is the subset of U)

B ⊂ U (B is the subset of U)

C ⊂ U (C is the subset of U)

Answer 2

Step-by-step explanation:

the set containing all objects or elements and of which all other sets are subsets.