# 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 $V$$U$, 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 $B$.

## Solved Examples on Universal Sets

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