REPRESENTATION OF 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.

Reading Notation :

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 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}

Representation of set in Different Forms

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.

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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

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