Selina solutions for Mathematics [English] Class 6 chapter 10 - Sets [Latest edition]

State whether or not the following elements form a set; if not, give reason:

All easy problems in your text book

State whether or not the following elements form a set; if not, give reason:

All three sided figures

State whether or not the following elements form a set; if not, give reason:

The first five counting numbers

State whether or not the following elements form a set; if not, give reason:

All the tall boys of your class

State whether or not the following elements form a set; if not, give reason:

The last three days of the week

State whether or not the following elements form a set; if not, give reason:

All triangles that are difficult to draw

State whether or not the following elements form a set; if not, give reason:

 The first three letters of the English alphabet

State whether or not the following elements form a set; if not, give reason:

All tasty fruits

State whether or not the following elements form a set; if not, give reason:

All clever boys of class 6

State whether or not the following elements form a set; if not, give reason:

All good schools in Delhi

State whether or not the following elements form a set; if not, give reason:

All the girls in your class, whose heights are less than your height

State whether or not the following elements form a set; if not, give reason:

All the boys in your class, whose heights are more than your height

State whether or not the following elements form a set; if not, give reason:

All the problems in your Mathematics book, which are difficult for Amit

If set A = {2, 3, 4, 5, 6}, state whether the following statement is true or false:

 2 ∈ A

If set A = {2, 3, 4, 5, 6}, state whether the following statement is true or false:

5, 6 ∈ A

If set A = {2, 3, 4, 5, 6}, state whether the following statement is true or false:

3, 4, 7 ∈ A

If set A = {2, 3, 4, 5, 6}, state whether the following statement is true or false:

2, 8 ∈ A

If set B = {4, 6, 8, 10, 12, 14}. State, which of the following statements is correct and which is wrong:

5 ∈ B

If set B = {4, 6, 8, 10, 12, 14}. State, which of the following statements is correct and which is wrong:

12 ∈ B

If set B = {4, 6, 8, 10, 12, 14}. State, which of the following statements is correct and which is wrong:

14 ∈ B

If set B = {4, 6, 8, 10, 12, 14}. State, which of the following statements is correct and which is wrong:

9 ∈ B

If set B = {4, 6, 8, 10, 12, 14}. State, which of the following statements is correct and which is wrong:

B is a set of even numbers between 2 and 16.

If set B = {4, 6, 8, 10, 12, 14}. State, which of the following statements is correct and which is wrong:

4,6 and 10 are die members of the set B. Also, write the wrong statements correctly.

State, whether true or false:

Sets {4, 9, 6,2} and {6, 2, 4, 9} are not the same

State, whether true or false:

Sets {0, 1, 3, 9, 4} and {4, 0, 1, 3, 9} are the same.

State, whether true or false:

Sets {5, 4} and {5, 4, 4, 5} are not the same

State, whether true or false:

Sets {8, 3} and {3, 3, 8} are the same

State, whether true or false:

Collection of vowels used in the word ‘ALLAHABAD’ forms a set

State, whether true or false:

If P is the set of letters in the word ‘ROOP’; then P = (p, o, r)

State, whether true or false:

If M is the set of letters used in the word ‘MUMBAI’, then: M = {m, u, b, a, i}

Write the set containing:

The first five counting numbers

Write the set containing:

The three types of angles

Write the set containing:

The three types of triangles

Write the set containing:

The members of your family

Write the set containing:

The first six consonants of the English Alphabet

Write the set containing:

The first four vowels of the English Alphabet

Write the set containing:

The names of any three Prime-Ministers of India.

Write the members (elements) of the set given below:

{3, 8, 5, 15, 12, 7}

Write the members (elements) of the set given below:

{c, m, n, o, s}

Write the sets whose elements are:

2, 4, 8, 16, 64 and 128

Write the sets whose elements are:

3, 5, 15, 45, 75 and 90

Write the set of letters used in the word ‘BHOPAL’.

Write the set of vowels used im the word ‘BENGAL’

Write the set of consonants used in the word ‘HONG KONG’.

Write the following set in the Roster Form:

The set of five numbers each of which is divisible by 3.

Write the following set in the Roster Form:

The set of integers between -4 and 4.

Write the following set in the Roster Form:

{x: x is a letter in the word ‘ SCHOOL’}

Write the following set in the Roster Form:

{x: x is an odd natural number between 10 and 20}

Write the following set in the Roster Form:

{Vowels used in the word ‘AMERICA’}

Write the following set in the Roster Form:

{Consonants used in the * word ‘MADRAS’}

Write the following set in the Roster Form:

All prime numbers between one and twenty

Write the following set in the Roster Form:

The squares of first four natural numbers

Write the following set in the Roster Form:

Even numbers between 1 and 9

Write the following set in the Roster Form:

First eight letters of the English alphabet

Write the following set in the Roster Form:

The letters of the word ‘BASKET’

Write the following set in the Roster Form:

Four cities of India whose names start with the letter J

Write the following set in the Roster Form:

Any four closed geometrical figures

Write the following set in the Roster Form:

Vowels used in the word ‘MONDAY’

Write the following set in the Roster Form:

Single digit numbers that are perfect squares as well

Write the given set in the Set-Builder Form:

{2, 4, 6, 8, 10}

Write the given set in the Set-Builder Form:

{2, 3, 5, 7, 11}

Write the given set in the Set-Builder Form:

{January, June, July}

Write the given set in the Set-Builder Form:

{a, e, i, o, u}

Write the given set in the Set-Builder Form:

{Tuesday, Thursday}

Write the given set in the Set-Builder Form:

{1,4,9, 16, 25}

Write the given set in the Set-Builder Form:

{5,10,15,20,25,30}

Write the following set in Roster (tabular) form and also in Set-Builder Form:

Set of all natural numbers that can divide 24 completely

Write the following set in Roster (tabular) form and also in Set-Builder Form:

Set of odd numbers between 20 and 35

Write the following set in Roster (tabular) form and also in Set-Builder Form:

Set of letters used in the word ‘CALCUTTA'

Write the following set in Roster (tabular) form and also in Set-Builder Form:

Set of names of the first five months of a year

Write the following set in Roster (tabular) form and also in Set-Builder Form:

Set of all two digit numbers that are perfect square as well

Write, in Roster Form, the set of:

The first four odd natural numbers each divisible by 5

Write, in Roster Form, the set of:

The counting numbers between 15 and 35; each of which is divisible by 6.

Write, in Roster Form, the set of:

The names of the last three days of a week

Write, in Roster Form, the set of:

The names of the last four months of a year

State, whether the given set is infinite or finite:

{3, 5, 7, ………}

State, whether the given set is infinite or finite:

{1, 2, 3, 4}

State, whether the given set is infinite or finite:

{………., -3, -2, -1, 0, 1, 2}

State, whether the given set is infinite or finite:

{20, 30, 40, 50, …, 200}

State, whether the given set is infinite or finite:

{7, 14, 21, ……….., 2401}

Is the following set is empty?

Set of counting numbers between 5 and 6

Is the following set is empty?

Set of odd numbers between 7 and 19

Is the following set is empty?

Set of odd numbers between 7 and 9

Is the following set is empty?

Set of even numbers which are not divisible by 2

Is the following set is empty?

{0}

State, whether the pair of sets, given below, are equal sets or equivalent sets:

{3, 5, 7} and {5, 3, 7}

State, whether the pair of sets, given below, are equal sets or equivalent sets:

{8, 6, 10, 12} and {3, 2, 4, 6}

State, whether the pair of sets, given below, are equal sets or equivalent sets:

{7, 7, 2, 1,2} and {1, 2, 7}

State, whether the pair of sets, given below, are equal sets or equivalent sets:

{2, 4, 6, 8, 10} and {a, b, d, e, m}

State, whether the pair of sets, given below, are equal sets or equivalent sets:

{5, 5, 2, 4} and {5, 4, 2, 2}

State, whether the following is a finite or infinite set:

Set of integers

State, whether the following is a finite or infinite set:

{Multiples of 5}

State, whether the following is a finite or infinite set:

{Fractions between 1 and 2}

State, whether the following is a finite or infinite set:

{Number of people in India}

State, whether the following is a finite or infinite set:

Set of trees in the world

State, whether the following is a finite or infinite set:

Set of leaves on a tree

State, whether the following is a finite or infinite set:

Set of children in all the schools of Delhi

State, whether the following is a finite or infinite set:

{ …….., -4, -2, 0, 2, 4, 6, 8}

State, whether the following is a finite or infinite set:

{- 12, – 9, – 6, – 3, 0, 3, 6, …….}

State, whether the following is a finite or infinite set:

{Number of points in a line segment 4 cm long}

State, whether or not the following set is empty:

{Prime numbers divisible by 2}

State, whether or not the following set is empty:

{Negative natural numbers}

State, whether or not the following set is empty:

{Women with height 5 metre}

State, whether or not the following set is empty:

{Integers less than 5}

State, whether or not the following set is empty:

{Prime numbers between 17 and 23}

State, whether or not the following set is empty:

Set of even numbers, not divisible by 2

State, whether or not the following set is empty:

Set of multiples of 3, which are more than 9 and less than 15

State, if the given pair of sets are equal sets or equivalent sets:

{Natural numbers less than five} and {Letters of the word ‘BOAT’}

State, if the given pair of sets are equal sets or equivalent sets:

{2, 4, 6, 8, 10} and {even natural numbers less than 12}

State, if the given pair of sets are equal sets or equivalent sets:

{1, 3, 5, 7, ………..} and set of odd natural numbers

State, if the given pair of sets are equal sets or equivalent sets:

{Letters of the word MEMBER} and {Letters of the word ‘REMEMBER’}

State, if the given pair of sets are equal sets or equivalent sets:

{Negative natural numbers} and {50th day of a month}

State, if the given pair of sets are equal sets or equivalent sets:

{Even natural numbers} and {odd natural numbers}

State, whether the following are finite or infinite sets:

{2, 4, 6, 8, …… 800}

State, whether the following are finite or infinite sets:

{……, -5, -4, -3, -2}

State, whether the following are finite or infinite sets:

{x : x is an integer between – 60 and 60}

State, whether the following are finite or infinite sets:

{No. of electrical appliances working in your house}

State, whether the following are finite or infinite sets:

{x : x is a whole number greater than 20}

State, whether the following are finite or infinite sets:

{x : x is a whole number less than 20}

For the statement, given below, write True or False:

{…., -8, -4, 0, 4, 8} is a finite set.

For the statement, given below, write True or False:

{ – 32, – 28, – 24, – 20, ……….. , 0, 4, 8, 16} is an infinite set

For the statement, given below, write True or False:

{x : x is a natural number less than 1} is the empty set

For the statement, given below, write True or False:

{Whole numbers between 15 and 16} = {Natural numbers between 5 and 6}

For the statement, given below, write True or False:

{Odd numbers divisible by 2} is the empty set

For the statement, given below, write True or False:

{Even natural numbers divisible by 3} is the empty set

For the statement, given below, write True or False:

{x : x is positive and x < 0} is the empty set.

For the statement, given below, write True or False:

{.., -5, -3, -1, 1, 3, 5, ..} is a finite set

State, giving reasons, whether the following pair of sets is a disjointed set or an overlapping set:

A = {Girls with ages below 15 years} and

B = {Girls with ages above 15 years}

State, giving reasons, whether the following pair of sets is a disjointed set or an overlapping set:

C = {Boys with ages above 20 years} and

D = {Boys with ages above 27 years}

State, giving reasons, whether the following pair of sets is a disjointed set or an overlapping set:

A = {Natural numbers between 35 and 60} and

B = {Natural numbers between 50 and 80}

State, giving reasons, whether the following pair of sets is a disjointed set or an overlapping set:

P = {Students of class IX studying in I.C.S.E. Board} and

Q = {Students of class IX}

State, giving reasons, whether the following pair of sets is a disjointed set or an overlapping set:

A = {Natural numbers multiples of 3 and less than 30} and

B = {Natural numbers divisible by 4 and between 20 and 45}

State, giving reasons, whether the following pair of sets is a disjointed set or an overlapping set:

P = {Letters in the word ‘ALLAHABAD’} and

Q = {Letters in the word ‘MISSOURI’}

Write the cardinal number of the following set:

A = {0, 1, 2, 4}

Write the cardinal number of the following set:

B = {-3, -1, 1, 3, 5, 7}

Write the cardinal number of the following set:

C = { }

Write the cardinal number of the following set:

D= {3, 2, 2, 1, 3, 1, 2}

Write the cardinal number of the following set:

E = {16, 17, 18 19}

Write the cardinal number of the following set:

F = {Whole numbers from 8 to 14}

Given:
A = {Natural numbers less than 10}
B = {Letters of the word ‘PUPPET’}
C = {Squares of first four whole numbers}
D = {Odd numbers divisible by 2}.

Find: n(A)

Given:
A = {Natural numbers less than 10}
B = {Letters of the word ‘PUPPET’}
C = {Squares of first four whole numbers}
D = {Odd numbers divisible by 2}.

Find: n(B)

Given:
A = {Natural numbers less than 10}
B = {Letters of the word ‘PUPPET’}
C = {Squares of first four whole numbers}
D = {Odd numbers divisible by 2}.

Find: n(C)

Given:
A = {Natural numbers less than 10}
B = {Letters of the word ‘PUPPET’}
C = {Squares of first four whole numbers}
D = {Odd numbers divisible by 2}.

Find: n(D)

Given:
A = {Natural numbers less than 10}
B = {Letters of the word ‘PUPPET’}
C = {Squares of first four whole numbers}
D = {Odd numbers divisible by 2}.

Find: A ∪ B AND n(A ∪ B)

Given:
A = {Natural numbers less than 10}
B = {Letters of the word ‘PUPPET’}
C = {Squares of first four whole numbers}
D = {Odd numbers divisible by 2}.

Find: A ∩ C AND n(A ∩ C)

Given:
A = {Natural numbers less than 10}
B = {Letters of the word ‘PUPPET’}
C = {Squares of first four whole numbers}
D = {Odd numbers divisible by 2}.

Find: n(B ∪ D)

Given:
A = {Natural numbers less than 10}
B = {Letters of the word ‘PUPPET’}
C = {Squares of first four whole numbers}
D = {Odd numbers divisible by 2}.

Find: n(C ∩ D)

Given:
A = {Natural numbers less than 10}
B = {Letters of the word ‘PUPPET’}
C = {Squares of first four whole numbers}
D = {Odd numbers divisible by 2}.

Find: n(B ∪ C)

Given:
A = {Natural numbers less than 10}
B = {Letters of the word ‘PUPPET’}
C = {Squares of first four whole numbers}
D = {Odd numbers divisible by 2}.

Find: n(A ∪ D)

State true or false for the following. Correct the wrong statement.

If A = {0}, then n(A) = 0

State true or false for the following. Correct the wrong statement.

n(Φ) = 1

State true or false for the following. Correct the wrong statement.

If T ={a, l, a, h, b, d, h), then n(T) = 5

State true or false for the following. Correct the wrong statement.

If B = {1, 5, 51, 15, 5, 1}, then n(B) = 6.