ROSTER FORM AND SET BUILDER NOTATION WORKSHEET

Question 1 :

List the elements of the following set in Roster form:

The set of all positive integers which are multiples of 7

Solution : 

The set of all positive integers which are multiples of 7 in roster form is

{7, 14, 21, 28,...........}

Question 2 :

List the elements of the following set in Roster form:

The set of all prime numbers less than 20.

Solution : 

The set of all prime numbers less than 20 in roster form is

{2, 3, 5, 7, 11, 13, 17, 19}

Question 3 :

Write the set A = { x : x is a natural number ≤ 8} in roster form.

Solution :

A = { x : x is a natural number ≤ 8}.

So, the set contains the elements 1, 2, 3, 4, 5, 6, 7, 8.

Hence in roster form A = {1, 2, 3, 4, 5, 6, 7, 8}

Question 4 :

Write the following set in roster form

A = {x : x ∈ N, 2 < x ≤ 10}

Solution :

A = {x : x ∈ N, 2 < x ≤ 10}

Set A will contain elements greater than 2 and less than or equal to 10.

A = { 3, 4, 5, 6, 7, 8, 9, 10}

Question 5 :

Write the following set in roster form

X =  {x : x = 2ⁿ, n ∈ N and n  ≤  5}

Solution :

X =  {x : x = 2ⁿ, n ∈ N and n  ≤  5}

To find the elements in the given set, we need to apply the values 1, 2, 3, 4 ,5 respectively instead of n.

X = { 2, 4, 8, 16, 32}

Question 6 :

Represent the following sets in set-builder form

X = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}

Solution :

X = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}

The set X contains all the days of a week.

Hence in set builder form, we write

X = { x : x is a day in a week }

Question 7 :

Represent the following sets in set-builder form

A = {1, 1/2, 1/3, 1/4, ...............}

Solution :

A = {1, 1/2, 1/3, 1/4, ...............}

The denominators of the elements are 1, 2, 3, 4, ......

The set-builder form is A = { x : x ,1/n, n ∈  N }

Question 8 :

Write the following sets in Set-Builder form

 The set of all positive even numbers

Solution :

A = The set of all positive even numbers

The set-builder form is

A = { x : x is a positive even number}

Question 9 :

Write the following sets in Set-Builder form

The set of all whole numbers less than 20

Solution :

A = The set of all whole numbers less than 20

The set-builder form is

A = {x : x is a whole number and x < 20}

Question 10 :

Write the following sets in Set-Builder form

The set of all positive integers which are multiples of 3

Solution :

A = The set of all positive integers which are multiples of 3

The set-builder form is

A = {x : x is a positive integer and multiple of 3}

Question 11 :

Let R be a relation from a set A to set B then:

(a) R = A U B    (b) R = A ∩ B    (c) R ≤ A×B    (d) R ≤ B×A

Solution :

Let A = {1, 2, 3} and B = {a, b}

A x B = {(1, a) (1, b) (2, a) (2, b) (3, a) (3, b)}

We may create many relations like this, so option c is correct.

Question 12 :

The number of subsets of a set containing n elements is:

(a) n    (b) 2^𝑛- 1    (c ) 𝑛²    (d) 2^𝑛

Solution :

Let us consider A = {1, 2, 3}

Subsets are = { }, {1}, {2}, {3}, {1, 2}, {2, 3}, {3, 1}, {1, 2, 3}

Number of elements (n) = 3

= 2³

Number of subsets are 8.

Question 13 :

If A = {1, 2, 3} , B = {1, 4, 6, 9}, and R is a relation from A to B defined by ‘x is greater than y ‘ the range of R is:

(a) {1, 4, 6, 9}     (b) {4,6,9}    (c) {1}    (d) None of these

Solution :

A = {1, 2, 3}  B = {1, 4, 6, 9}

R = {(9, 2) (9, 3) (6, 2)(6, 3)(4, 2)(4, 1) (4, 3)}

Range = {4, 6, 9}

So, option b is correct.

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