Answer
Verified
480.6k+ views
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 .
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 .
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Change the following sentences into negative and interrogative class 10 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE