NCERT Solutions for Class 11 Math Chapter 1 - Sets

Question 1:

The collection of all months of a year beginning with letter J.

Question 2:

The collection of ten most talented writers of India.

Question 3:

A team of eleven best cricket batsmen of the world.

Question 4:

The set of all boys in your class.

Question 5:

The collection of all natural numbers less than 100.

Question 6:

A collection of novels written by the writer Munshi Prem Chand.

Question 7:

The collection of all even integers.

Question 8:

The collection of questions in this chapter.

Question 9:

A collection of most dangerous animals of the world.

Question 10:

Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces.
5 ........ A

Question 11:

Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces.
8 .......... A

Question 12:

Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces.
0 .............. A

Question 13:

Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces.
4 ........ A

Question 14:

Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces.
2 .......... A

Question 15:

Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces.
10 .............. A

Question 16:

Write the following sets in the roaster form :
A = {x : x is an integer and – 3 $\le$ x < 7}.

Question 17:

Write the following sets in the roaster form :
B = {x : x is a natural number less than 6}.

Question 18:

Write the following sets in the roaster form :
C = {x : x is a two-digit natural number such that
sum of its digits is 8}.

Question 19:

Write the following sets in the roaster form :
D = {x : x is a prime number, which is a divisor of 60}.

Question 20:

Write the following sets in the roaster form :
E = the set of all letters in the word
‘TRIGONOMETRY’.

Question 21:

Write the following sets in the roaster form :
F = the set of all letters of the word ‘BETTER’.

Question 22:

List all the elements of the following sets :
A = {x : x is an odd natural number}.

Question 23:

List all the elements of the following sets :

Question 24:

List all the elements of the following sets :
C = {x : x is an integer, x2 $\le$ 4}.

Question 25:

List all the elements of the following sets :
D = {x : x is a letter in the word ‘LOYAL’}.

Question 26:

List all the elements of the following sets :
E = {x : x is a month of a year not having 31days}

Question 27:

List all the elements of the following sets :
F = {x : x is a consonant in the English alphabet word which precedes k}.

Question 28:

Match each of the sets on the left in the roster form with the same set on the right described in the set builder form.

Question 29:

Which of the following are examples of the null set ?
Set of odd natural numbers divisible by 2.

Question 30:

Which of the following are examples of the null set ?
{x : x is a natural number, x < 5 and x> 7}.

Question 31:

Which of the following are examples of the null set ?
{y : y is a point common to any two parallel lines}.

Question 32:

Which of the following sets are finite or infinite ?
The set of months of a year

Question 33:

Which of the following sets are finite or infinite ?
{1, 2, 3, .............}

Question 34:

Which of the following sets are finite or infinite ?
{1, 2, 3, ............, 99, 100}

Question 35:

Which of the following sets are finite or infinite ?
The set of positive integers greater than 100

Question 36:

Which of the following sets are finite or infinite ?
The set of prime numbers less than 99

Question 37:

State whether each of the following sets is finite or infinite :
The set of lines, which are parallel to the x-axis.

Question 38:

State whether each of the following sets is finite or infinite :
The set of letters in English alphabet.

Question 39:

State whether each of the following sets is finite or infinite :
The set of numbers, which are multiples of 5.

Question 40:

State whether each of the following sets is finite or infinite :
The set of animals living on earth.

Question 41:

State whether each of the following sets is finite or infinite :
The set of circles through origin (0, 0).

Question 42:

In the following, state whether A = B or not :
A = {a, b, c, d}, B = {d, c, b, a}.

Question 43:

In the following, state whether A = B or not :
A = {4, 8, 12, 16}, B = {8, 4, 16, 18}.

Question 44:

In the following, state whether A = B or not :
A = {2, 4, 6, 8, 10},
B = {x : x is a positive even integer and x $\le$ 10}

Question 45:

In the following, state whether A = B or not :
A = {x : x is multiple of 10},
B = {10, 15, 20, 25, 30, .........}.

Question 46:

Are the following pair of sets equal ? Give reasons :
A = {2, 3}, B = {x : x is a solution of
x² + 5x + 6 = 0}.

Question 47:

Are the following pair of sets equal ? Give reasons :
A = {2, 3}, B = {x : x is a solution of
x² + 5x + 6 = 0}.

Question 48:

Are the following pair of sets equal ? Give reasons :
A = {x : x is a letter of the word FOLLOW},
B = {x : x is a letter of the word WOLF}.

Question 49:

From the sets, given below, select examples of equal sets :
A = {2, 4, 8, 12}, B = {1, 2, 3, 4},
C = {4, 8, 12, 14}, D = {3, 1, 4, 2},
E = {– 1, 1}, F = {0, 0},
G = {1, – 1}, H = {0, 1}.

Question 50:

Make correct statements by filling in the symbols
‘$\subset$’ or ‘⊄’ in the blank spaces :
{2, 3, 4} ............... {1, 2, 3, 4, 5}

Question 51:

Make correct statements by filling in the symbols
‘$\subset$’ or ‘⊄’ in the blank spaces :
{a, b, c} ............... {b, c, d}

Question 52:

Make correct statements by filling in the symbols
‘$\subset$’ or ‘⊄’ in the blank spaces :
{x : x is a student of Class XI of your school}
........... {x : x is a student of your school}

Question 53:

Make correct statements by filling in the symbols
‘$\subset$’ or ‘⊄’ in the blank spaces :
{x : x is a circle in the plane} ............ {x : x is a
circle with radius 1}

Question 54:

Make correct statements by filling in the symbols
‘$\subset$’ or ‘⊄’ in the blank spaces :
{x : x is a triangle in the plane} ............. {x : x is
a rectangle in the plane}

Question 55:

Make correct statements by filling in the symbols
‘$\subset$’ or ‘⊄’ in the blank spaces :
{x : x is an equilateral triangle in the plane}...........
{x : x is a triangle in the plane}

Question 56:

Make correct statements by filling in the symbols
‘$\subset$’ or ‘⊄’ in the blank spaces :
{x : x is an even natural number}.......... {x : x is
an integer}.

Question 57:

Examine whether the following statements are true or false :
{a, b} ⊄ {b, c, a}

Question 58:

Examine whether the following statements are true or false :
{a, e} $\subset$ {x : x is a vowel in the English alphabet}

Question 59:

Examine whether the following statements are true or false :
{1, 3, 5} $\subset$ {1, 3, 5}

Question 60:

Examine whether the following statements are true or false :
{a} $\subset$ {a, b, c}

Question 61:

Examine whether the following statements are true or false :
{a} $\in$ {a, b, c}

Question 62:

Examine whether the following statements are true or false :
{x : x is an even natural number less than 6}
$\subset$ {x : x is a natural number which divides 36}

Question 63:

Let A = {1, 2, {3, 4}, 5}. Which of the following statements are correct and why ?
{3, 4} $\subset$ A

Question 64:

Let A = {1, 2, {3, 4}, 5}. Which of the following statements are correct and why ?
{3, 4} $\in$ A

Question 65:

Let A = {1, 2, {3, 4}, 5}. Which of the following statements are correct and why ?
{{3, 4}} $\subset$ A

Question 66:

Let A = {1, 2, {3, 4}, 5}. Which of the following statements are correct and why ?
1 $\in$ A

Question 67:

Let A = {1, 2, {3, 4}, 5}. Which of the following statements are correct and why ?
1 $\subset$ A

Question 68:

Let A = {1, 2, {3, 4}, 5}. Which of the following statements are correct and why ?
{1, 2, 5} $\subset$ A

Question 69:

Let A = {1, 2, {3, 4}, 5}. Which of the following statements are correct and why ?
{1, 2, 5} $\in$ A

Question 70:

Let A = {1, 2, {3, 4}, 5}. Which of the following statements are correct and why ?
{1, 2, 3} $\subset$ A

Question 71:

Let A = {1, 2, {3, 4}, 5}. Which of the following statements are correct and why ?
$\mathrm{\varphi }$ $\in$ A

Question 72:

Let A = {1, 2, {3, 4}, 5}. Which of the following statements are correct and why ?
$\mathrm{\varphi }$ $\subset$ A

Question 73:

Let A = {1, 2, {3, 4}, 5}. Which of the following statements are correct and why ?
{$\mathrm{\varphi }$} $\subset$ A

Question 74:

Write down all the subsets of the following sets : {a}

Question 75:

Write down all the subsets of the following sets : {a, b}

Question 76:

Write down all the subsets of the following sets : {1, 2, 3}

Question 77:

Write down all the subsets of the following sets : $\mathrm{\varphi }$

Question 78:

How many elements has P (A) if A = $\mathrm{\varphi }$ ?

Question 79:

Write the following as intervals :
{x : x $\in$ R, – 4 < x $\le$ 6}

Question 80:

Write the following as intervals :
{x : x $\in$ R, – 12 < x < – 10}

Question 81:

Write the following as intervals :
{x : x $\in$ R, 0 $\le$ x < 7}

Question 82:

Write the following as intervals :
{x : x $\in$ R, 3 $\le$ x $\le$ 4}

Question 83:

Write the following intervals in set-builder form : (– 3, 0)

Question 84:

Write the following intervals in set-builder form : [6, 12]

Question 85:

Write the following intervals in set-builder form : (6, 12]

Question 86:

Write the following intervals in set-builder form : [– 23, 5)

Question 87:

What universal set would you propose for each of the following ?
(i) The set of right-triangles.
(ii) The set of isosceles triangles.

Question 88:

Given the sets :
A = {1, 3, 5}, B = {2, 4, 6}, C = {0, 2, 4, 6, 8}.
Which of the following may be considered as universal set(s) for all the three sets A, B and C ?
(i) {0, 1, 2, 3, 4, 5, 6}
(ii) $\mathrm{\varphi }$
(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
(iv) {1, 2, 3, 4, 5, 6, 7, 8}.

Question 89:

Find the union of each of the following pairs of sets : X = {1, 3, 5}, Y = {1, 2, 3}

Question 90:

Find the union of each of the following pairs of sets :
A = {a, e, i, o, u}, B = {a, b, c}

Question 91:

Find the union of each of the following pairs of sets :
A = {x : x is a natural number and multiple of 3},
B = {x : x is a natural number less than 6}

Question 92:

Find the union of each of the following pairs of sets :
A = {x : x is a natural number and 1 < x $\le$ 6}
B = {x : x is a natural number and 6 < x < 10}.

Question 93:

Find the union of each of the following pairs of sets :
A = {1, 2, 3}, B = $\mathrm{\varphi }$.

Question 94:

Let A = {a, b} and B = {a, b, c}.
Is A $\subset$ B ? What is A $\mathrm{\upsilon }$ B ?

Question 95:

If A and B are two sets such that A $\subset$ B, then what is A $\mathrm{\upsilon }$ B ?

Question 96:

A = {1, 2, 3, 4}, B = {3, 4, 5, 6},
C = {5, 6, 7, 8} and D = {7, 8, 9, 10}.
Find :A $\mathrm{\upsilon }$ B

Question 97:

A = {1, 2, 3, 4}, B = {3, 4, 5, 6},
C = {5, 6, 7, 8} and D = {7, 8, 9, 10}.
Find :A $\mathrm{\upsilon }$ C

Question 98:

A = {1, 2, 3, 4}, B = {3, 4, 5, 6},
C = {5, 6, 7, 8} and D = {7, 8, 9, 10}.
Find : B $\mathrm{\upsilon }$ C

Question 99:

A = {1, 2, 3, 4}, B = {3, 4, 5, 6},
C = {5, 6, 7, 8} and D = {7, 8, 9, 10}.
Find : B $\mathrm{\upsilon }$ D

Question 100:

A = {1, 2, 3, 4}, B = {3, 4, 5, 6},
C = {5, 6, 7, 8} and D = {7, 8, 9, 10}.
Find : A $\mathrm{\upsilon }$ B $\mathrm{\upsilon }$ C

Question 101:

A = {1, 2, 3, 4}, B = {3, 4, 5, 6},
C = {5, 6, 7, 8} and D = {7, 8, 9, 10}.
Find : A $\mathrm{\upsilon }$ B $\mathrm{\upsilon }$ D

Question 102:

A = {1, 2, 3, 4}, B = {3, 4, 5, 6},
C = {5, 6, 7, 8} and D = {7, 8, 9, 10}.
Find : B $\mathrm{\upsilon }$ C $\mathrm{\upsilon }$ D

Question 103:

Find the intersection of each pair of sets of question:
X = {1, 3, 5}, Y = {1, 2, 3}

Question 104:

Find the intersection of each pair of sets of question:
A = {a, e, i, o, u}, B = {a, b, c}

Question 105:

Find the intersection of each pair of sets of question:
A = {x : x is a natural number and multiple of 3},
B = {x : x is a natural number less than 6}

Question 106:

Find the intersection of each pair of sets of question:
A = {x : x is a natural number and 1 < x ≤ 6}
B = {x : x is a natural number and 6 < x < 10}.

Question 107:

Find the intersection of each pair of sets of question:
A = {1, 2, 3}, B = $\mathrm{\varphi }$.

Question 108:

If A = {3, 5, 7, 9, 11} and
B = {7, 9, 11, 13},
C = {11, 13, 15}, D = {15, 17} ;
find : A $\cap$ B

Question 109:

If A = {3, 5, 7, 9, 11} and
B = {7, 9, 11, 13},
C = {11, 13, 15}, D = {15, 17} ;
find : B $\cap$ C

Question 110:

If A = {3, 5, 7, 9, 11} and
B = {7, 9, 11, 13},
C = {11, 13, 15}, D = {15, 17} ;
find : A $\cap$ C $\cap$ D

Question 111:

If A = {3, 5, 7, 9, 11} and
B = {7, 9, 11, 13},
C = {11, 13, 15}, D = {15, 17} ;
find : A $\cap$ C

Question 112:

If A = {3, 5, 7, 9, 11} and
B = {7, 9, 11, 13},
C = {11, 13, 15}, D = {15, 17} ;
find : B $\cap$ D

Question 113:

If A = {3, 5, 7, 9, 11} and
B = {7, 9, 11, 13},
C = {11, 13, 15}, D = {15, 17} ;
find : A $\cap$ (B $\mathrm{\upsilon }$ C)

Question 114:

If A = {3, 5, 7, 9, 11} and
B = {7, 9, 11, 13},
C = {11, 13, 15}, D = {15, 17} ;
find : A $\cap$ D

Question 115:

If A = {3, 5, 7, 9, 11} and
B = {7, 9, 11, 13},
C = {11, 13, 15}, D = {15, 17} ;
find :A $\cap$ (B $\mathrm{\upsilon }$ D)

Question 116:

If A = {3, 5, 7, 9, 11} and
B = {7, 9, 11, 13},
C = {11, 13, 15}, D = {15, 17} ;
find :(A $\cap$ B) $\cap$ (B $\mathrm{\upsilon }$ C)

Question 117:

If A = {3, 5, 7, 9, 11} and
B = {7, 9, 11, 13},
C = {11, 13, 15}, D = {15, 17} ;
find : (A $\mathrm{\upsilon }$ D) $\cap$ (B $\mathrm{\upsilon }$ C)

Question 118:

Let A = {x : x is a natural number},
B = {x : x is an even natural number},
C = {x : x is an odd natural number},
D = {x : x is a prime number}. Find :
A $\cap$ B

Question 119:

Let A = {x : x is a natural number},
B = {x : x is an even natural number},
C = {x : x is an odd natural number},
D = {x : x is a prime number}. Find :
A $\cap$ C

Question 120:

Let A = {x : x is a natural number},
B = {x : x is an even natural number},
C = {x : x is an odd natural number},
D = {x : x is a prime number}. Find :
A $\cap$ D

Question 121:

Let A = {x : x is a natural number},
B = {x : x is an even natural number},
C = {x : x is an odd natural number},
D = {x : x is a prime number}. Find :
B $\cap$ C

Question 122:

Let A = {x : x is a natural number},
B = {x : x is an even natural number},
C = {x : x is an odd natural number},
D = {x : x is a prime number}. Find :
B $\cap$ D

Question 123:

Let A = {x : x is a natural number},
B = {x : x is an even natural number},
C = {x : x is an odd natural number},
D = {x : x is a prime number}. Find :
C $\cap$ D

Question 124:

Which of the following pairs of sets are disjoint ?
{1, 2, 3, 4} and
{x : x is a natural number and 4 ≤ x ≤ 6}

Question 125:

Which of the following pairs of sets are disjoint ?
{a, e, i, o, u} and {c, d, e, f}

Question 126:

Which of the following pairs of sets are disjoint ?
{x : x is an even integer} and
{x : x is an odd integer}.

Question 127:

Let A = {3, 6, 9, 12, 15, 18, 21},
B = {4, 8, 12, 16, 20},
C = {2, 4, 6, 8, 10, 12, 14, 16} and
D = {5, 10, 15, 20}.
Find : A – B

Question 128:

Let A = {3, 6, 9, 12, 15, 18, 21},
B = {4, 8, 12, 16, 20},
C = {2, 4, 6, 8, 10, 12, 14, 16} and
D = {5, 10, 15, 20}.
Find :A – C

Question 129:

Let A = {3, 6, 9, 12, 15, 18, 21},
B = {4, 8, 12, 16, 20},
C = {2, 4, 6, 8, 10, 12, 14, 16} and
D = {5, 10, 15, 20}.
Find : A – D

Question 130:

Let A = {3, 6, 9, 12, 15, 18, 21},
B = {4, 8, 12, 16, 20},
C = {2, 4, 6, 8, 10, 12, 14, 16} and
D = {5, 10, 15, 20}.
Find :B – A

Question 131:

Let A = {3, 6, 9, 12, 15, 18, 21},
B = {4, 8, 12, 16, 20},
C = {2, 4, 6, 8, 10, 12, 14, 16} and
D = {5, 10, 15, 20}.
Find :C – A

Question 132:

Let A = {3, 6, 9, 12, 15, 18, 21},
B = {4, 8, 12, 16, 20},
C = {2, 4, 6, 8, 10, 12, 14, 16} and
D = {5, 10, 15, 20}.
Find :D – A

Question 133:

Let A = {3, 6, 9, 12, 15, 18, 21},
B = {4, 8, 12, 16, 20},
C = {2, 4, 6, 8, 10, 12, 14, 16} and
D = {5, 10, 15, 20}.
Find :B – C

Question 134:

Let A = {3, 6, 9, 12, 15, 18, 21},
B = {4, 8, 12, 16, 20},
C = {2, 4, 6, 8, 10, 12, 14, 16} and
D = {5, 10, 15, 20}.
Find :B – D

Question 135:

Let A = {3, 6, 9, 12, 15, 18, 21},
B = {4, 8, 12, 16, 20},
C = {2, 4, 6, 8, 10, 12, 14, 16} and
D = {5, 10, 15, 20}.
Find :C – B

Question 136:

Let A = {3, 6, 9, 12, 15, 18, 21},
B = {4, 8, 12, 16, 20},
C = {2, 4, 6, 8, 10, 12, 14, 16} and
D = {5, 10, 15, 20}.
Find :D – B

Question 137:

Let A = {3, 6, 9, 12, 15, 18, 21},
B = {4, 8, 12, 16, 20},
C = {2, 4, 6, 8, 10, 12, 14, 16} and
D = {5, 10, 15, 20}.
Find :C – D

Question 138:

Let A = {3, 6, 9, 12, 15, 18, 21},
B = {4, 8, 12, 16, 20},
C = {2, 4, 6, 8, 10, 12, 14, 16} and
D = {5, 10, 15, 20}.
Find :D – C

Question 139:

If X = {a, b, c, d} and Y = {f, b, d, g}, find :
X – Y

Question 140:

If X = {a, b, c, d} and Y = {f, b, d, g}, find :
Y – X

Question 141:

If X = {a, b, c, d} and Y = {f, b, d, g}, find :
X $\cap$ Y

Question 142:

If R is the set of real numbers and Q is the set of rational numbers, then what is R – Q ?

Question 143:

State whether each of the following statement is
true or false. Justify your answer.
{2, 3, 4, 5} and {3, 6} are disjoint sets.

Question 144:

State whether each of the following statement is
true or false. Justify your answer.
{a, e, i, o, u} and {a, b, c, d} are disjoint sets.

Question 145:

State whether each of the following statement is true or false. Justify your answer.
{2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets.

Question 147:

State whether each of the following statement is true or false. Justify your answer.
{2, 6, 10} and {3, 7, 11} are disjoint sets.

Question 148:

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9},
A = { 1, 2, 3, 4},
B = {2, 4, 6, 8}, C = {3, 4, 5, 6}.
Find : A′

Question 149:

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9},
A = { 1, 2, 3, 4},
B = {2, 4, 6, 8}, C = {3, 4, 5, 6}.
Find : B′

Question 150:

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9},
A = { 1, 2, 3, 4},
B = {2, 4, 6, 8}, C = {3, 4, 5, 6}.
Find : (A $\mathrm{\upsilon }$ C)′

Question 151:

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9},
A = { 1, 2, 3, 4},
B = {2, 4, 6, 8}, C = {3, 4, 5, 6}.
Find : (A $\mathrm{\upsilon }$ B)′

Question 152:

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9},
A = { 1, 2, 3, 4},
B = {2, 4, 6, 8}, C = {3, 4, 5, 6}.
Find : (A′)′

Question 153:

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9},
A = { 1, 2, 3, 4},
B = {2, 4, 6, 8}, C = {3, 4, 5, 6}.
Find : (B – C)′

Question 154:

If U = {a, b, c, d, e, f, g, h}, find the complement of the following sets :
A = {a, b, c}, B = {d, e, f, g}, C = {a, c, e, g}, D = {f, g, h, a}.

Question 155:

Taking the set of natural numbers as universal set, write down the complements of the following sets :
{x : x is an even number}

Question 156:

Taking the set of natural numbers as universal set, write down the complements of the following sets :
{x : x is an odd number}

Question 157:

Taking the set of natural numbers as universal set, write down the complements of the following sets :
{x : x is a positive multiple of 3}

Question 158:

Taking the set of natural numbers as universal set, write down the complements of the following sets :
{x : x is a prime number}

Question 159:

Taking the set of natural numbers as universal set, write down the complements of the following sets :
{x : x is a natural number divisible by 3 and 5}

Question 160:

Taking the set of natural numbers as universal set, write down the complements of the following sets :
{x : x is a perfect square}

Question 161:

Taking the set of natural numbers as universal set, write down the complements of the following sets :
{x : x is a perfect cube}

Question 162:

Taking the set of natural numbers as universal set, write down the complements of the following sets :
{x : x + 5 = 8}

Question 163:

Taking the set of natural numbers as universal set, write down the complements of the following sets :
{x : 2x + 5 = 9}

Question 164:

Taking the set of natural numbers as universal set, write down the complements of the following sets :
{x : x > 7}

Question 165:

Taking the set of natural numbers as universal set, write down the complements of the following sets :
{x : x $\in$ N and 2x + 1 > 10}

Question 166:

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9},
A = {2, 4, 6, 8},
B = {2, 3, 5, 7}. Verify that :
(A $\mathrm{\upsilon }$ B)′ = A′ $\cap$ B′

Question 167:

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9},
A = {2, 4, 6, 8},
B = {2, 3, 5, 7}. Verify that :
(A $\cap$ B)′ = A′ $\cap$ B′

Question 168:

Draw appropriate Venn diagram for each of the following :
(A $\mathrm{\upsilon }$ B)′

Question 169:

Draw appropriate Venn diagram for each of the following :
A′ $\cap$ B′

Question 170:

Draw appropriate Venn diagram for each of the following :
(A $\cap$ B)′

Question 171:

Draw appropriate Venn diagram for each of the following :
A′ $\mathrm{\upsilon }$ B′

Question 172:

Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60°, what is A′ ?

Question 173:

Fill in the blanks to make each of the following a true statement :
A $\mathrm{\upsilon }$ A′ = .........

Question 174:

Fill in the blanks to make each of the following a true statement :
$\mathrm{\varphi }$′ $\cap$ A = .........

Question 175:

Fill in the blanks to make each of the following a true statement :
A $\cap$ A′ = .........

Question 176:

Fill in the blanks to make each of the following a true statement :
U′ $\cap$ A = .........

Question 177:

If X, Y are two sets such that :
n (X) = 17, n (Y) = 23 and n (X $\mathrm{\upsilon }$ Y) = 38,
find n (X $\cap$ Y).

Question 178:

If X and Y are two sets such that X $\mathrm{\upsilon }$ Y has 18 elements, X has 8 elements and Y has 15 elements, how many elements does X $\cap$ Y have ?

Question 179:

In a group of 400 people, 250 can speak Hindi and 200 can speak English. How many people can speak both Hindi and English ?

Question 180:

If S and T are two sets such that S has 21 elements, T has 32 elements and S $\cap$ T has 11 elements, how many elements does S $\mathrm{\upsilon }$ T have ?

Question 181:

If X and Y are two sets such that X has 40 elements, X $\mathrm{\upsilon }$ Y has 60 elements and X $\cap$ Y has 10 elements, how many elements does Y have ?

Question 182:

In a group of 70 people, 37 like coffee, 52 like tea and each person likes atleast one of the two drinks. How many like both coffee and tea ?

Question 183:

In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis only and not cricket ? How many like tennis ?

Question 184:

In a committee 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. How many speak atleast one of these two languages ?

Question 185:

Write the solution set of the equation :
x² + x – 2 = 0
in roster form.

Question 186:

Write the set {x : x is a positive integer and x² < 40} in the roster form.

Question 187:

Write the set {1, 4, 9, 16, 25, ....} in the set builder form.

Question 188:

Write the set

in the set builder form.

Question 189:

Which of the following sets are finite and infinite :
{x : x $\in$ N and (x – 1)(x – 2) = 0}

Question 190:

Which of the following sets are finite and infinite :
{x : x $\in$ N and x² = 4}

Question 191:

Which of the following sets are finite and infinite :
{x : x $\in$ N and 2x – 1 = 0}

Question 192:

Which of the following sets are finite and infinite :
{x : x $\in$ N and x is prime}

Question 193:

Which of the following sets are finite and infinite :
{x : x $\in$ N and x is odd}.

Question 194:

Find the pairs of equal sets from the following sets, if any, giving reasons :
A = {0}, B = {x : x > 15 and x < 5},
C = {x : x – 5 = 0}, D = {x : x² = 25},
E = {x : x is an integral positive root of the equation x² – 2x – 15 = 0}.

Question 195:

Which of the following pairs of sets are equal ? Justifiy your answer.
X, the set of letters in ‘ALLOY’ and B, the set of letters in ‘LOYAL’

Question 196:

Which of the following pairs of sets are equal ? Justifiy your answer.
A = {n : n $\in$ Z and n² ≤ 4} and
B = {x : x $\in$ R and x² – 3x + 2 = 0}.

Question 197:

Consider the following sets :
$\mathrm{\varphi }$, A = {1, 3}, B = {1, 5, 9}, C = {1, 3, 5, 7, 9}.
Insert the correct symbol $\subset$ or ⊄ between each pair of sets :
$\mathrm{\varphi }$.......B

Question 198:

Consider the following sets :
$\mathrm{\varphi }$, A = {1, 3}, B = {1, 5, 9}, C = {1, 3, 5, 7, 9}.
Insert the correct symbol $\subset$ or ⊄ between each pair of sets :
A.........B

Question 199:

Consider the following sets :
$\mathrm{\varphi }$, A = {1, 3}, B = {1, 5, 9}, C = {1, 3, 5, 7, 9}.
Insert the correct symbol $\subset$ or ⊄ between each pair of sets :
A..........C

Question 200:

Consider the following sets :
$\mathrm{\varphi }$, A = {1, 3}, B = {1, 5, 9}, C = {1, 3, 5, 7, 9}.
Insert the correct symbol $\subset$ or ⊄ between each pair of sets :
B..........C

Question 201:

Let A = {a, e, i, o, u} and B = {a, b, c, d}.
Is A a subset of B ? Is B a subset of A ?

Question 202:

Let A, B and C be three sets. If A $\in$ B and B $\subset$ C, is it true that A $\subset$ C ? If not, give an example.

Question 203:

Let A = {2, 4, 6, 8} and B = {6, 8, 10, 12}.
Find A $\mathrm{\upsilon }$ B.

Question 204:

Let A = {a, e, i, o, u} and B = {a, i, u}.
Show that A $\mathrm{\upsilon }$ B = A.

Question 205:

Let X = {Ram, Geeta, Akbar} be the set of students of Class XI, who are in school hockey team. Let Y = {Geeta, David, Ashok} be the set of students from class XI who are in school football team. Find X$\mathrm{\upsilon }$Y and interpret the set.

Question 206:

Let A = {2, 4, 6, 8} and B = {6, 8, 10, 12}. Find A $\cap$ B.

Question 207:

Let X = {Ram, Geeta, Akbar} be the set of students of Class XI, who are in school hockey team. Let Y = {Geeta, David, Ashok} be the set of students from class XI who are in school football team. Find X $\cap$ Y.

Question 208:

Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and
B = {2, 3, 5, 7}. Find A $\cap$ B and hence show that A $\cap$ B = B.

Question 209:

Let A = {1, 2, 3, 4, 5, 6}, B = {2, 4, 6, 8}.
Find A–B and B–A.

Question 210:

Let V = {a, e, i, o, u} and B = {a, i, k, u}.
Find V – B and B – V.

Question 211:

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and
A = {1, 3, 5, 7, 9}. Find A′.

Question 212:

Let U be universal set of all students of class XI of a co-educational school and A be the set of girls in class XI. Find A′.

Question 213:

Let U = {1, 2, 3, 4, 5, 6}, A = {2, 3}
and B = {3, 4, 5}. Find A′, B′, A′ $\cap$ B′, A $\mathrm{\upsilon }$ B and
hence show that (A $\mathrm{\upsilon }$ B)′ = A′ $\cap$ B′.

Question 214:

If X and Y are two sets such that X $\mathrm{\upsilon }$ Y has 50 students, X has 28 elements and Y has 32 elements, how many elements does X $\cap$ Y have ?

Question 215:

In a school there are 20 teachers who teach Mathematics or Physics. Of these, 12 teach Mathematics and 4 teach both Physics and Mathematics. How many teach Physics ?

Question 216:

In a class of 35 students, 24 like to play cricket and 16 like to play football. Also, each student likes to play atleast one of the two games. How many students like to play both cricket and football ?

Question 217:

In a survey of 400 students in a school, 110 were listed as taking Apple Juice, 140 as taking Orange Juice and 85 were listed as taking both Apple as well as orange Juice. Find how many students were taking neither Apple juice nor Orange Juice.

Question 218:

There are 200 individuals with a skin disorder. 120 had been exposed to the chemical C₁, 50 to chemical C₂ and 30 to both the chemicals C₁ and C₂. Find the number of individuals exposed to : Chemical C₁ but not Chemical C₂

Question 219:

There are 200 individuals with a skin disorder. 120 had been exposed to the chemical C₁, 50 to chemical C₂ and 30 to both the chemicals C₁ and C₂. Find the number of individuals exposed to : Chemical C₂ but not Chemical C₁

Question 220:

There are 200 individuals with a skin disorder. 120 had been exposed to the chemical C₁, 50 to chemical C₂ and 30 to both the chemicals C₁ and C₂. Find the number of individuals exposed to : Chemical C₁ or Chemical C₂.

Question 221:

Show that the set of letters needed to spell “CATARACT” and the set of letters needed to spell “TRACT” are equal.

Question 222:

List all the subsets of the set {–1, 0, 1}.

Question 223:

Show that A $\mathrm{\upsilon }$ B = A $\cap$ B implies A = B.

Question 224:

For any sets A and B, show that :
P(A $\cap$ B) = P(A) $\cap$ P(B).

Question 225:

A market research group conducted a survey of 1000 consumers and reported that 720 consumers liked product A and 450 liked product B. What is the least number that must have liked both products ?

Question 226:

A market research group conducted a survey of 1000 consumers and reported that 720 consumers liked product A and 450 liked product B. What is the least number that must have liked both products ?

Question 227:

Out of 500 car owners investigated, 400 owned car A and 200 owned car B, 50 owned both A and B cars. Is this data correct ?

Question 228:

A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to a total of 58 men and only three men got medals in all the three sports, how many received medals in exactly two of the three sports ?