Sets in Mathematics

Sets in Mathematics

In real life, we often come across collection of objects viz.

#Cricket Team

#Pack of Cards

#Members of a Club

In mathematics, we also come across collections, examples are.

#Odd natural numbers

#Even natural numbers

#Numbers which is divisible by 3 and less than 20.

If you observe each example is well-defined collection of objects. It means that we can clearly tell whether an object belongs to a collection or not.

From the above examples and observation we can define a set.


Set-       A set is a well-defined collection of objects.


Sets are usually denoted by capital letters A, B, C, D,……..

Elements are members of a set  are usually represented by small letters a, b, c, d,……

Representation of Sets-

There are two methods to represent a set.

1- Tabular or Roster form

2- Set-Builder form

  • In tabular form  all the elements of a set are listed and separated by  comma, and are enclosed within curly braces { }.

Example-  V={a, e,  i , o ,u}

  • In set-builder form the same set would  be written

V={x: x is a vowel in English alphabets}

See the explanation in video

 

See examples in the post

Tabular (Roster) Form and Set-Builder Form

 

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