- Real Numbers
- 6 Write Five Rational Numbers Greater Than 2 Composite
- Integers
- Rational Numbers Calculator
- Rational Numbers Definition
- 6 Write Five Rational Numbers Greater Than 22
- 6 Write Five Rational Numbers Greater Than 24
Roster Form :
A rational number is any whole number, fraction, mixed number or decimal, including their negative counterparts. An example of a rational number is 8.5. It is rational because it can be turned into a simple fraction of 8 1 ⁄ 2. Ex 1.2, 3 - Chapter 1 Class 8 Rational Numbers - NCERT Solutions Write 5 rational numbers smaller than 2? To find rational numbers, let us draw a number line Now, numbers on the left of number line are smaller than 2 Thus, 5 rational numbers which are smaller than 2 are: 3, 2, 1, 0, & 1.
Listing the elements of a set inside a pair of braces { } is called the roster form.
(i) Let A be the set of even natural numbers less than 11.
In roster form we write A = {2, 4, 6, 8, 10}
(ii) A = {x : x is an integer and- 1≤ x < 5}
In roster form we write A = {-1, 0,1, 2, 3, 4}
Try to translate 4 0 0 – quickly translated. Let us look into some examples in roster form.
Set Builder Form :
Set-builder notation is a notation for describing a set by indicating the properties that its members must satisfy.
Reading Notation :
‘|’or ‘:’ such that
A = { x : x is a letter in the word dictionary }
We read it as
“A is the set of all x such that x is a letter in the word dictionary”
For example,
(i) N = 'x : x is a natural number,
(ii) P = 'x : x is a prime number less than 100,
(iii) A = 'x : x is a letter in the English alphabet,
Here we are going to see examples on roster form and set builder form.
Roster Form Examples
Example 1 :
List the elements of the following set in Roster form:
The set of all positive integers which are multiples of 7
Solution :
The set of all positive integers which are multiples of 7 in roster form is
{7, 14, 21, 28,......}
Example 2 :
List the elements of the following set in Roster form:
The set of all prime numbers less than 20.
Solution :
The set of all prime numbers less than 20 in roster form is
{2, 3, 5, 7, 11, 13, 17, 19}
Example 3 :
Write the set A = { x : x is a natural number ≤ 8} in roster form.
Solution :
A = { x : x is a natural number ≤ 8}.
So, the set contains the elements 1, 2, 3, 4, 5, 6, 7, 8.
Hence in roster form A = {1, 2, 3, 4, 5, 6, 7, 8}
Real Numbers
Example 4 :
Write the following set in roster form
A = {x : x ∈ N, 2 < x ≤ 10}
Solution :
A = {x : x ∈ N, 2 < x ≤ 10}
Set A will contain elements greater than 2 and less than or equal to 10.
A = { 3, 4, 5, 6, 7, 8, 9, 10}
Example 5 :
Write the following set in roster form
X = {x : x = 2n, n ∈ N and n ≤5}
Solution :
X = {x : x = 2n, n ∈ N and n ≤5}
To find the elements in the given set, we need to apply the values 1, 2, 3, 4 ,5 respectively instead of n.
n = 1 x = 2n x = 21 x = 2 | n = 2 x = 2n x = 22 x = 4 | n = 3 x = 2n x = 23 x = 8 | n = 4 x = 2n x = 24 x = 16 | n = 5 x = 2n x = 25 x = 32 |
X = { 2, 4, 8, 16, 32}
Set Builder Form Examples
Example 1 :
Represent the following sets in set-builder form
X = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}
Solution :
X = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}
The set X contains all the days of a week.
Hence in set builder form, we write
X = { x : x is a day in a week }
Example 2 :
Represent the following sets in set-builder form
6 Write Five Rational Numbers Greater Than 2 Composite
A = {1, 1/2, 1/3, 1/4, ........}
Solution :
![Numbers Numbers](https://s3mn.mnimgs.com/img/shared/content_ck_images/ck_5c9e379c26f48.jpeg)
A = {1, 1/2, 1/3, 1/4, ........}
The denominators of the elements are 1, 2, 3, 4, ...
The set-builder form is A = { x : x ,1/n, n ∈ N }
Example 3 :
Integers
Write the following sets in Set-Builder form
Rational Numbers Calculator
The set of all positive even numbers
Solution :
A = The set of all positive even numbers
The set-builder form is
![Rational Rational](https://d1avenlh0i1xmr.cloudfront.net/8db7893f-4b70-4f52-a1b1-fef1d0efdfd3slide27.jpg)
A = { x : x is a positive even number}
Example 4 :
Write the following sets in Set-Builder form
The set of all whole numbers less than 20
Solution :
A = The set of all whole numbers less than 20
The set-builder form is
A = {x : x is a whole number and x < 20}
Example 5 :
Write the following sets in Set-Builder form
The set of all positive integers which are multiples of 3
Solution :
A = The set of all positive integers which are multiples of 3
The set-builder form is
A = {x : x is a positive integer and multiple of 3}
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Rational Numbers Definition
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OTHER TOPICS
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6 Write Five Rational Numbers Greater Than 22
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6 Write Five Rational Numbers Greater Than 24
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