Sets Representation | Roster and Set-Builder Form

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So today's topic is :-

Set Representation

How can we represent a set?

A set can be represented in 2 ways:-

1) Roster Form and

2) Set-Builder Form

Roster/Tabular Form

• In it, all the elements of a set are listed being separated by a comma and are enclosed within braces { }.
• For eg. The set of all even positive integers less than 7 can be represented as

                                 A={2,4,6}

NOTE:

1. The order in which all the elements are listed is immaterial i.e. {1,2,3} = {2,3,1} .It means that the order in which we put the elements in a set doesn't matters.

2. Elements that repeat are taken only once.     

{s, c, h, o, o, l} = {s, c, h, o, l}

Set-Builder Form

• In it, all the elements of set posses a single common property which is not possessed by any element outside the set.

• For eg. The set of all even positive integers less than 7 can be represented as

                    A = { x : x < 7 and x ϵ N}

                                    OR

                 A = {x : x is a natural number and x<7 }

Practice

1) Write the following sets in roster form:

a) C = {x : x is a 2-digit natural no. such that the sum of its digits is 8 }

Ans. Since,  1+7 =8 , 2+6=8, 3+5=8, 4+4 =8 and 8+0=8

          Therefore,  C = { 17, 26, 35, 44, 53 , 62, 71, 80 }.

b) E = The set of all letters in the word “ TRIGONOMETRY ”

Ans. Since we don’t repeat any element.

         Therefore,  E = { T, R, I, G, O ,N , M, E, Y }

2) Write the following sets in Set-Builder form:

a){ 3, 6, 9, 12}

Ans. Since, 3 = 3 * 1 , 6 = 3 * 2, 9 = 3 * 3 and 12 = 3 * 4

         Therefore, { x : x = 3 * n and 1 < x < 4 }

b) { 1, 2 , 3, 4, 5, 6}

        2   3  4   5  6  7

Ans. Since, all the denominators are just incremented form of numerators like d = n+1.

         Therefore,

        { x : x = n   where n ϵ N and 1 < n< 6 } 

                      n+1

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