Problems on set-I

            In this page 'Problems on set-I' we are going to see problems on set definitions, element of a set, writing in set builder form, in Roster form and in Descriptive form.

           Parents and teachers can guide the students to do the problems on their own. If they are having any doubt they can verify the solutions.

Problems on set-I

The 5 problems we are going to discuss below are based on the definition of set.

1. Which of the following are sets? Justify your answer.

(i)Collection of good books.

(ii)Collection of prime numbers less than 30.

(iii)The collection of ten most talented mathematics teachers.

(iv)The collection of all students in your school.

(v)The collection of all even numbers.


 Next 5 problems are based on the elements of a set.

2. Let A={0,1,2,3,4,5}. Insert the appropriate symbol ∈ or ∉ in the blank spaces.

(i)  0 ----- A

(ii) 6 ----- A

(iii) 3-----A

(iv) 4----- A

(v) 7-------A


         The problems under  3, 4 and 5 are based on set notations. 

3.Write the following sets in Set-builder form.

(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 'AMERICA'


4. Write the following sets in the Roster form.

(i) A={x:xℕ, 2< x ≤ 10}

(ii)B = {x:xℤ, -1/2 < x < 11/2}

(iii) C = {x:x is a prime number and a divisor of 6}

(iv) D = {x:x=2ⁿ, nℕ and n ≤ 5}

(v) E = {x:x=2y-1, y≤ 5, y∈W}

(vi) F= {x:x is an integer, x²≤ 16}.


5. Write the following sets in Descriptive form.

(i)A= {a,e, i, o, u}


(iii) C ={1,4,9,16,25}

(iv) D ={x:x is a letter in the word, 'SET THEORY'}

(v) E ={x:x is a prime number between 10 and 20}


                     Students can try to solve the problems on their own. Parents and teachers can encourage the students to do so. If they are having any doubt they can verify the Solutions.  If you are having any further doubt you can contact us through mail, we will help you to clear your doubt.

                                     Set Theory


Featured Categories 

Math Word Problems

SAT Math Worksheet

P-SAT Preparation

Math Calculators

Quantitative Aptitude


Algebraic Identities

Trig. Identities


Multiplication Tricks


Types of Angles

Aptitude Test