**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.

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 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 }

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 }

(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 "Representation of a set".

Apart from the stuff given above, if you want to know more about "Representation of a set", please click here

Apart from the stuff, "Representation of a set", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**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**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**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 **

**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 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**