How To Make Set Builder Notation

SET BUILDER NOTATION

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}

Solved Problems

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 = 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 = 2 ⁿ

x = 2¹

x = 2

n = 2

x = 2 ⁿ

x = 2²

x = 4

n = 3

x = 2 ⁿ

x = 2³

x = 8

n = 4

x = 2 ⁿ

x = 2⁴

x = 16

n = 5

x = 2 ⁿ

x = 2⁵

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}

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us :

v4formath@gmail.com

We always appreciate your feedback.

You can also visit the following web pages on different stuff in math.

WORD PROBLEMS

HCF and LCM word problems

Word problems on simple equations

Word problems on linear equations

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and Venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree