# Describe the following set in set – builder form.

$A=\left\{ 1,2,3,4,5,6 \right\}.$

Answer

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**Hint:**The set builder notation of any set \[A\] is given as $A=\{x:\text{property of x}\} $.

**Complete Step by Step Answer:**

Here , we mention the property of the elements of the set .

We know that set builder notation is a notation in which the set is described by using the properties of the elements .

For example : Consider the set \[B=\{2,4,6,8,10\}\]. Here $B$ is a set of elements which are positive and even numbers less than \[12\]. So , the property of the elements of the set is that they are positive even numbers less than \[12\]. So , the set $B$ is represented in set builder form as $B =\left\{x:x\text{ is positive even number} < 12\right\}$ .

Now , we are given the set $A$.

The elements of the given set $A$ are $A=\left\{ 1,2,3,4,5,6 \right\}$

We can clearly see that the elements are natural numbers which are less than $7$.

Now , we know that set builder notation is a notation in which the set is described by using the properties of the elements .

So , here in set $A$, we can see the property of the elements is that they are natural numbers less than $7$.

**So , in set builder form, we can write the set $A$ as $A=\left\{ x:x\text{ is natural number }<7 \right\}$.**

**Note:**The set builder form is read as “$A$ is the set of all $x$ such that $x$ is a natural number less than $7$”. Students generally get confused between set builder notation of sets and roster notation of sets . Both are different and hence , should not be confused . This confusion can lead to wrong answers .

Last updated date: 25th Sep 2023

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