Universal Set

Definition of Universal Set

An Universal Set of any set say A or B, may be defined as the set, that contains all the elements of set A or B, including its own elements without repetitions.

Symbol of Universal Set

There is no standard notation for the Universal Sets, but the most commonly used symbols for Universal Sets are VU, and ξ.

Explanation of Universal Set

To understand the concept of Universal Set, let us consider a set A that consists of 4 elements as,

A = \{1, 2, 3, 4\}

And, let us consider another set B which also consists of 4 elements as,

B = \{9, 10, 11, 12\}

Then, the Universal Set U, will consist of all the elements present in set A and set B and also its own elements. Therefore, an Universal Set of the given two sets A and B will be,

U = \{1, 2, 3, 4, 9, 10, 11, 12, 13, 14\}

However, it is not necessary for an Universal Set to have its own elements. It can also be formed only by the elements of the sets A and B.

Venn Diagram of Universal Set

The figure below shows the Venn Diagram for Universal Set of the above two sets A and B.

Universal Set Venn Diagram

Solved Examples on Universal Sets

The universal set U will contain all the elements of set A and set B.
Therefore, Universal set, U={a, b, c, d, r, s, t}

The universal set U will have all the elements of A, B and C.
Therefore, U={1, 2, 3, 4, 5, 6, 7, 9, 10}

Frequently Asked Questions (FAQ)

An Universal Set of any set say A or B, is the set, that contains all the elements of set A or B, including its own elements without repetitions.

An Universal Set of any set say A or B, is the set, that contains all the elements of set A or B, including its own elements without repetitions.

The universal set U of any set A is the set that contains all the elements of A including its own elements.

However, Set A is called the subset of B if all the elements of set A is present in the set B.

The Cardinality of a Universal Set is the number of elements present in the set. Let U is a universal set of any set and it contains 15 elements, then the Cardinality of the set U is, n(U)=15.

Example of Universal Set:

Let us consider two sets A and B such that,

A={a, b, c, d} and B={e, f}

Then one of the universal set U of A and B will be,

U={a, b, c, d, e, f}

Superset: Set A is called Superset of B if all the elements of B is present in A.

Universal Set: An Universal set is the set that contains all the elements or sets that can be formed.

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