# SET BUILDER FORM WORKSHEET

## About "Set builder form worksheet"

Set builder form worksheet :

Set builder form worksheet is much useful to the students who woulds like to practice problems on set theory.

## Set builder form worksheet - Problems

(i)  The set of all positive even numbers

(ii)  The set of all whole numbers less than 20

(iii)  The set of all positive integers which are multiples of 3

(iv)  The set of all odd natural numbers less than 15

(v)  The set of all letters in the word ‘computer’

## Set builder form worksheet - Answers

(i)  {x : x is a positive even number}

(ii)  {x : x is a whole number and x < 20}

(iii)  {x : x is a positive integer and multiple of 3}

(iv)  {x : x is an odd natural number and x < 15}

(v)   {x : x is a letter in the word 'computer'}

To understand and solve the problems given in the above worksheet, we have to know the stuff "Representation of a set".

Now, let us look at the stuff "Representation of a set".

## Representation of a set

Set can be represented in any one of the following three ways or forms.

(i)  Descriptive form

(ii)  Set-builder form or Rule form

(iii)  Roster form or Tabular form

Let us discuss the above different forms representation of a set in detail.

## Descriptive form

One way to specify a set is to give a verbal description of its elements.

This is known as the descriptive form of specification.

The description must allow a concise determination of which elements belong to the set and which elements do not.

For example,

(i) The set of all natural numbers.

(ii) The set of all prime numbers less than 100.

(iii) The set of all letters in English alphabets.

## Set-Builder Form or Rule Form

Set-builder notation is a notation for describing a set by indicating the properties that its members must satisfy.

A  =  { x : x is a letter in the word "dictionary" }

“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 or Tabular Form

Listing the elements of a set inside a pair of braces {  } is called the roster form.

For example,

(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 }

## Important points

(i)  In roster form each element of the set must be listed exactly once. By convention, the elements in a set should not be repeated.

(ii)  Let A be the set of letters in the word “coffee”,

That is,  A  =  { c, o, f, e }. So, in roster form of the set A the following are invalid.

{ c, o, e } -------> (not all elements are listed)

{ c, o, f, f, e } -------> (element ‘f’ is listed twice)

(iii)  In a roster form the elements in a set can be written in any order.

The following are valid roster form of the set containing the elements 2, 3 and 4.

{ 2, 3, 4 }

{ 2, 4, 3 }

{4, 3, 2 }

Each of them represents the same set.

(iv)  If there are either infinitely many elements or a large finite number of elements, then three consecutive dots called ellipsis are used to indicate that the pattern of the listed elements continues, as in  { 5, 6, 7,...... }  or  { 3, 6, 9, 12, 15,........60 }.

(v) Ellipsis can be used only if enough information has been given so that one can figure out the entire pattern.

After having gone through the stuff given above, we hope that the students would have understood "Set builder form worksheet".

Apart from the stuff, "Set builder form worksheet", if you need any other stuff in math, please use our google custom search here.

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear 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 fractrions

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

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6