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”
Examples :
(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}
Problem 1 :
Describe the following sets in set builder form.
A = {1, 2, 3, 4, 5, 6}
Solution :
The given set contains set of natural numbers. But it ends up with 6. So, we may represent the given set in set builder form as follows.
A = {x : x is a natural number ≤ 6}
Problem 2 :
Write the following set in roster form
B = {1, 1/2, 1/3, 1/4, 1/5,................}
Solution :
The elements of the above set is in the form 1/n. The denominator is set of natural numbers.So, we may represent the given set in set builder form as follows.
B = {x : x = 1/n, n ∈ N}
Problem 3 :
Write the following set in roster form
X = {x : x = 2^{n}, n ∈ N and n ≤ 5}
Solution :
X = {x : x = 2^{n}, 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 = 2^{n} x = 2^{1} x = 2 |
n = 2 x = 2^{n} x = 2^{2} x = 4 |
n = 3 x = 2^{n} x = 2^{3} x = 8 |
n = 4 x = 2^{n} x = 2^{4} x = 16 |
n = 5 x = 2^{n} x = 2^{5} x = 32 |
X = {2, 4, 8, 16, 32}
Problem 4 :
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 }
Problem 5 :
Represent the following sets in set-builder form
A = {January, February, March, ............, December}
Solution :
A = {January, February, March, ............, December}
The set A contains all the months of a year.
Hence in set builder form, we write
X = {x : x is a months of a year}
Problem 6 :
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}
Problem 7 :
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}
Problem 8 :
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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