Math Doubts

Representation of sets

A method of representing a collection of well-defined objects is called the representation of a set.


Mathematics is all about geometrical shapes and study of them in mathematical approach. So, a set is usually represented in two different methods.

  1. Graphical representation
  2. Mathematical representation

Let’s study both methods for learning how to represent sets in mathematics.


Now, learn the concept of representing a set from basic and advanced examples.

Basic example

A set of some fruits.

  1. Apple
  2. Banana
  3. Grape
  4. Orange
  5. Strawberry

All of the given objects are fruits. So, the collection of them is a set.

Graphical representation

graphical representation of set

A set or a collection of well-defined objects are represented graphically by displaying all the objects inside closed geometrical figures, like a triangle, a circle, an ellipse, a rectangle, a square, and etc.

In this case, the objects are apple, banana, grape, orange and strawberry. A set of fruits is displayed graphically by displaying all the objects inside a closed geometrical shape. Thus, a set is represented graphically in mathematics.

Mathematical representation

A set is also represented mathematically by displaying the names of all objects with comma separation inside a pair of curly braces (brackets).

$\Big\{\, Apple, Banana, Grape, Orange, Strawberry \,\Big\}$

Thus, a set or a collection of well-defined objects are represented in mathematics.

Advanced example

A set of first five natural numbers.

example of representation of set

$1, 2, 3, 4,$ and $5$ are first five natural numbers. Display the first five natural numbers inside any closed geometrical shape for representing this set graphically.

Similarly, write the first five natural numbers with comma separation inside the curly braces.

$\Big\{\, 1, 2, 3, 4, 5 \,\Big\}$

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