Sets

of sets is used for the foundation of various topics in mathematics.

To learn sets we often talk about the collection of objects, such as a set of vowels, set of negative numbers, a group of friends, a list of fruits, a bunch of keys, etc.

What is set (in mathematics)?

The collection of well-defined distinct objects is known as a set. The word well-defined refers to a specific property which makes it easy to identify whether the given object belongs to the set or not. The word ‘distinct’ means that the objects of a set must be all different.

For example:

1. The collection of children in class VII whose weight exceeds 35 kg represents a set.

2. The collection of all the intelligent children in class VII does not
represent a set because the word intelligent is vague. What may appear
intelligent to one person may not appear the same to another person.

Elements of Set:

The different objects that form a set are called the elements of a set.
The elements of the set are written in any order and are not repeated.
Elements are denoted by small letters.

Notation of a Set:

A set is usually denoted by capital letters and elements are denoted by small letters

If x is an element of set A, then we say x ϵ A. [x belongs to A]

If x is not an element of set A, then we say x ∉ A. [x does not belong to A]

For example:

The collection of vowels in the English alphabet.

Solution :

Let us denote the set by V, then the elements of the set are a, e, i, o, u or we can say, V = [a, e, i, o, u].

We say a ∈ V, e ∈ V, i ∈ V, o ∈ V and u ∈ V.

Also, we can say b ∉ V, c ∉ v, d ∉ v, etc.