examples of sets that can be written in roster form but not in set builder form and vice versa
Answers
Answer:
Roster Form and Set Builder Form :
Here we are going to see how to represent sets in roster form and set builder form.
Roster form :
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}
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,
Roster form and set builder form - Examples
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}
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 6 :
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 7 :
Represent the following sets in set-builder form
A = {1, 1/2, 1/3, 1/4, ...............}
Solution :
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 8 :
Write the following sets in Set-Builder form
The set of all positive even numbers
Solution :
A = The set of all positive even numbers
The set-builder form is
A = { x : x is a positive even number}
Example 9 :
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 10 :
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}