Sets Class 11

teachoo
Ex 1.1,1
Which of the following are sets? Justify our answer.
(i) The collection of all months of a year beginning with the
letter J.
We can count the months of the year beginning with J.
(January, June, July)
This cannot be changed. Thus, it is well defined.
Thus, this is a set

Which of the following are sets? Justify our answer.
(ii) The collection of ten most talented writers of India.

Which of the following are sets? Justify our answer.
(iii) A team of eleven best–cricket batsmen of the world.

Which of the following are sets? Justify our answer.
(iv) The collection of all boys in your class.

Which of the following are sets? Justify our answer.
(v) The collection of all natural numbers less than 100.

Which of the following are sets? Justify our answer.
(vi) A collection of novels written by the writer Munshi Prem Chand.

Which of the following are sets? Justify our answer.
(vii) The collection of all even integers.

Which of the following are sets? Justify our answer.
(viii) The collection of questions in this Chapter.

Which of the following are sets? Justify our answer.
(ix) A collection of most dangerous animals of the world.

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Ex 1.1, 2
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol € or ¢ in
the blank spaces:
(I) 5..A
As Sis in set A. €— belongs to
SEA ¢ — does not belongs to

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Ex 1.1, 3
Write the following sets in roster form:
(i) A= {x: x is an integer and —3 <x < 7}.
Integers = ......-4, —3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10...
The elements of this set are —3, —2, -1, 0, 1, 2, 3, 4, 5, and 6 only.
A={-3,-2,-1, 0, 1, 2, 3, 4, 5, 6}

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

Write the following sets in roster form:
(iii) C = {x: x is a two–digit natural number such that the sum of its digits is 8}

Write the following sets in roster form:
(iv) D = {x: x is a prime number which is divisor of 60}

Write the following sets in roster form:
(v) There are 12 letters in the word TRIGONOMETRY. out of which letters T,R, and O are repeated.

Write the following sets in roster form:
(vi) F = The set of all letters in the word BETTER.

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Ex 1.1, 4
Write the following sets in the set—builder form:
(i) {3, 6, 9, 12}

3=3x1

6=3x2

9=3x3

12=3x4
{x:x=3n,n€Nand1<n<4}

Write the following sets in the set–builder form:
(ii) {2, 4, 8, 16, 32}

Write the following sets in the set–builder form:
(iii) {5, 25, 125, 625}

Write the following sets in the set–builder form:
(iv) {2, 4, 6 …}

Write the following sets in the set–builder form:
(v) {1,4,9,….100}

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Ex 1.1,5
List all the elements of the following sets:
(i) A = {x: x is an odd natural number}
Natural numbers = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,....
Odd Natural numbers = 1, 3, 5, 7, 8, 11,....
So, the elements of this set are 1, 3, 5, 7, 9, 11,...
Hence, A= {1, 3,5, 7, Dy}

List all the elements of the following sets:
(ii) B = {x: x is an integer, −1/2 < x < 9/2}

List all the elements of the following sets:
(iii) C = {x: x is an integer, x2 ≤ 4}

List all the elements of the following sets:
(iv) D = {x: x is a letter in the word “LOYAL”}

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

List all the elements of the following sets:
(vi) F = {x: x is a consonant in the English alphabet which proceeds k}.

Ex 1.1, 6 teachoo.com
Match each of the set on the left in the roster form with the same
set on the right described in set—builder form:
(i) {1, 2, 3, 6} (a) {x : x is a prime number and a divisor of 6}
(ii) {2, 3} wy {x : x is an odd natural number less than 10}
(iii) {M,A,T,H,E,1,C,S} (c) {x x is natural number and divisor of 6}
(iv) {1, 3, 5, 7, 9} (d) {x : x is a letter of the word MATHEMATICS}.
: x is a prime number and a divisor of 6}

6=6x1

6=3x2
1, 2, 3, 6 are divisors of 6,
out of which 2, 3 are prime
So, (ii) matches (a)

teachoo

Ex 1.2, 1
Which of the following are examples of the null set
(i) Set of odd natural numbers divisible by 2

Null set (Q)} :

Which has no elements
Natural numbers = 1, 2, 3, 4, 5, 6,.....
Odd natural numbers = 1, 3, 5, 7, 9,...
No odd number is divisible by 2,
Therefore there are no elements in this set.
« Itis a null set.

Which of the following are examples of the null set
(ii) Set of even prime numbers

Which of the following are examples of the null set
(iii) {x: x is a natural numbers, x < 5 and x > 7 }

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

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Ex 1.2, 2
Which of the following sets are finite or infinite
(i) The set of months of a year
The months of a year are
January, February, March, April, May, June, July, August,
September, October, November, December.
There are 12 months in a year, so the set has 12 elements.
Therefore, the set is finite.

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

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

Which of the following sets are finite or infinite
(iv) The sets of positive integers greater than 100

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

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Ex 1.2, 3
State whether each of the following set is finite or infinite:
(i) The set of lines which are parallel to the x-axis

Y

: a

y’
There are infinite lines parallel to x- axis,
so the set will have infinite elements.
So, our set is infinite.

State whether each of the following set is finite or infinite:
(ii) The set of letters in the English alphabet

State whether each of the following set is finite or infinite:
(iii) The set of numbers which are multiple of 5

State whether each of the following set is finite or infinite:
(iv) The set of animals living on the earth

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

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Ex 1.2, 4
In the following, state whether A = B or not:
(i) A = {a, b, c, d}; B = {d, c, b, a}
Element of Set A =a, b,c, d
Element of Set B =a, b, c, d
Each element of Ais the same as each element of B,

~A=B

In the following, state whether A = B or not:
(ii) A = {4, 8, 12, 16}; B = {8, 4, 16, 18}

In the following, state whether A = B or not:
(iii) A = {2, 4, 6, 8, 10}; B = {x: x is positive even integer and x ≤ 10}

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

Ex 1.2,5 teachoo.com
Are the following pair of sets equal? Give reasons.
(i) A = {2, 3}; B = {x: x is solution of x? + 5x+ 6 = 0}
A= {2, 3}
B = {x: x is a solution of x? + 5x + 6 = O}
Solving x? + 5x + 6 = 0,

x? + 2x +3x+6=0

x(x + 2} + 3(x+2)=0

(x + 2)(x + 3)=0

X=—2 orx=—3
» B= {-2,-3}

Are the following pair of sets equal? Give reasons
(ii) A = {x: x is a letter in the word FOLLOW};
B = {y: y is a letter in the word WOLF}

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Ex 1.2, 6
From the sets given below, select 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, a},
G={1, -1}, H = {0, 1}
Set A has 4 elements,
So, Ais not equal to sets E, F, G, H
Also, elements of Set A are not in B, C, D
So, Ais not equal to set B, C, D

teachoo

Ex 1.3, 1
Make correct statements by filling in the symbols € or ¢ in the
blank spaces:
(i) (2,3, 4} .. 1, 2,3, 4, 5} c-is a subset

Z- is not a subset

Ac Bif all elements of Aare inB
Since set {1, 2, 3, 4,5} has all the
elements of set {2, 3, 4}
So, {2, 3, 4} is a subset of {1, 2, 3, 4, 5}

+. {2, 3, 4} c {1, 2, 3, 4, 5}

Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces:
(ii) {a, b, c} … {b, c, d}

Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces:
(iii) {x: x is a student of Class XI of your school} … {x: x student of your school}

Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces:
(iv) {x: x is a circle in the plane} … {x: x is a circle in the same plane with radius 1 unit}

Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces:
(v) {x: x is a triangle in a plane}…{x: x is a rectangle in the plane}

Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces:
(vi) {x: x is an equilateral triangle in a plane} … {x: x is a triangle in the same plane}

Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces:
(vii) {x: x is an even natural number} … {x: x is an integer}

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Ex 1.3, 2
Examine whether the following statements are true or false:
(i) {a, b} € {b, c, a}

C-is a subset

¢-is not a subset

AC Bif all elements of Aare in B
Since, each element of {a, b} is also an element of {b, c, a}.
So, {a, b} C {b, c, a}
So, the statement is False

Examine whether the following statements are true or false:
(ii) {a, e} ⊂ {x: x is a vowel in the English alphabet}

Examine whether the following statements are true or false:
(iii) {1, 2, 3} ⊂ {1, 3, 5}

Examine whether the following statements are true or false:
(iv) {a} ⊂ {a, b, c}

Examine whether the following statements are true or false:
(v) {a} ∈ {a, b, c}

Examine whether the following statements are true or false:
(vi) {x: x is an even natural number less than 6}
⊂ {x: x is a natural number which divides 36}

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Ex 1.3, 3
Let A = {1, 2, {3, 4}, 5}. Which of the following statements are
incorrect and why?
(i) {3, 4} CA
Here, A= {1, 2, (3, 4,}5} C- is a subset

AC Bif all elements of Aare in B
Let {3, 4}=x
So, A= {1, 2, x, 5}
3,4 isin {3, 4} but not inA
So, {3, 4} is not a subset of A
So, the given statement is incorrect.

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Ex 1.3, 4
Write down all the subsets of the following sets:
(i) {a}
Let A = {a}
Number of elements in Ais 1
Hence n=1
Number of subsets of A = 2"

=?!

=2
Null set and the set itself are the subsets of the set.
The subsets of {a} are @ and {a}.

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

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

Write down all the subsets of the following sets:
(iv) ϕ

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Ex 1.3,5
Write the following as intervals:
(i) {x:x ER, -4<x <6}
({) Not included
[] included
{x: x € R, -4 <x < 6} = (-4, 6]

Write the following as intervals:
(ii) {x: x ∈ R, –12 < x < –10}

Write the following as intervals:
(iii) {x: x ∈ R, 0 ≤ x< 7}

Write the following as intervals:
(iv) {x: x∈ R, 3 ≤ x ≤ 4}

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Ex 1.3, 6
Write the following intervals in set-builder form:
(i) (-3, 0)
() Not included
[ ] included
All real numbers between —3 and 0 are included
but -3,0 not included
-3<x<0
And interval form is valid for real numbers.
{-3, 0) = («: x ER, -3< x < 0}

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

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

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

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Ex 1.3, 7
What universal set (s) would you propose for each of the following:
(i) The set of right triangles

Universal set

The set of all triangles must contain Containing all elements
all elements of the set of right triangles.
So we propose set of all triangles as universal set.

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Ex 1.3, 8
Given the sets A = {1, 3, 5}, B= {2, 4, 6} and C = {0, 2,4, 6, 8},
which of the following may be considered as universals set(s) for all
the three sets A, Band C
(i) {0, 1, 2, 3, 4, 5, 6}

Universal set

Elements of A+B +C = (1, 3, 5, 2, 4, 6, 0, 8}
The given set does not contain 8,
So it cannot be universal set for A, B and C.

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Ex 1.3, 5
How many elements has P(A), if A= ?
P(A) is the power set of set A
Number of elements of P(A} = 2"
where n is the number of elements of the set A
Given A = ¢, then number of elements of set A = 0.
-. Number of elements of P(A) = 2"

= 20

=1
Hence, P(A) has one element.

teachoo
Ex1.4,1
Find the union of each of the following pairs of sets:
(i) X = {1, 3, 5} ¥ = {1, 2, 3}
U Union - Combination of two sets
XUY={1, 3, 5} U {1, 2, 3}

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

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

Find the union of each of the following pairs of sets:
(iv) A = {x: x is a natural number and 1 < x ≤ 6}
B = {x: x is a natural number and 6 < x < 10}

Find the union of each of the following pairs of sets:
(v) A = {1, 2, 3}, B = ∅

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Ex 1.4, 2
Let A = fa, b}, B = {a, b, c}. Is AC B? What is A U BP
A= {a, b} U Union - Combination of two sets
B= {a, b, c} C Subset - A C B (all elements of set A in set B)
Every element of A is in B.
So, Ais a subset of B
ie. ACB.
AU B= {a, b} U {a, b, c}

= {a, b, c}

Ex 1.4, 3 (INTRODUCTION) teachoo.com
lf A and B are two sets such that A C B, then what is A U B?
Introduction({Example)
Let’s take an example
A={1, 2}
B= {1, 2, 3}
Every element of A is in B.
So, Ais a subset of B
ie. ACB.
AU B=({1, 2}U {1, 2, 3}
={1, 2, 3}
=B

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Ex 1.4, 4

If A= {1, 2, 3, 4},

B = {3, 4, 5, 6},

C= {5, 6, 7, 8} and

D = {7, 8, 9, 10}; find
{I) AUB
AUB= (1, 2, 3, 4} U {3, 4, 5, 6}

={1, 2,3, 4,5, 6}

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Ex 1.4,5
Find the intersection of each pair of sets:
(i) X = {1, 3, 5}, Y = {1, 2, 3}
/N Intersection — Common of two sets
X NY ={1,3,5} 9 {1,2,3}
= {1, 3}

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Ex 1.4, 6

If A= {3, 5, 7, 9, 11},

B={7, 9, 11, 13},

C= {11, 13, 15} and

D={15, 17}; find
(i) ANB
ANB ={3,5, 7,9, 11} 9 {7, 9, 11, 13}

={7,9, 11}

Ex 1.4,7 teackoo.com
If A= {x: x is a natural number},
B ={x: x is an even natural number},
C= {x: x is an odd natural number}
and D = {x: x is a prime number},
Find
First, let’s write all the sets in roster form
A= {x: x is a natural number}
={1,2,3,4,5..}
B = {x:x is an even natural number}
= {2,4,6,8...}

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Ex 1.4, 8
Which of the following pairs of sets are disjoint
(i) {1, 2, 3, 4} and {x: x is a natural number and 4 < x < 6}
Two sets are disjoint if they have no common element
n Intersection — Common of two sets
If AO B= @, then sets are disjoint
Natural number = 1, 2, 3, 4, 5, 6, 7, 8, 9, ..
{x: x is a natural number and 4 < x < 6} = {4, 5, 6}
Now, {1, 2, 3, 4} 9 {4, 5, 6} = {4}
#0

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

Which of the following pairs of sets are disjoint
(iii) {x: x is an even integer} and {x: x is an odd integer}

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Ex 1.4, 9
If A = {3, 6, 9,12, 15, 18, 21}, B = {4, 8, 12, 16, 20},
C= {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}; find
(i) A-B
A-B=A-(ANB)
/N Intersection — Common of two sets
A-B=A-{(ANMB}
A B= {3, 6, 9,12, 15, 18, 21} m {4, 8, 12, 16, 20}
= {12}
A-B=A-{(ANMB}
= {3, 6,9, 12, 15, 18, 21}- {12}
= {3, 6, 9, 15, 18, 21}

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Ex 1.4, 10
If X = fa, b, c, d} and Y = ff, b, d, g}, find
(i) X-Y
A-B=A—(ANB)

X-Y=X-(XY) Nn Intersection — Common of two sets
XN Y= {b, d}
X-Y=X-(XnNY)

= {a, b, c, d}—{b, d}

= {a, c}

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Ex 1.4, 10
If X = {a, b, c, d} and Y = {f, b, d, g}, find
(ii) Y-X
A-B=A-(ANB)
/N Intersection — Common of two s
Y¥-X=Y¥-(Y¥ NX}
XN Y={b, d}
Y-X=Y-(YNX)}
= tf, b, d, g}— {b, d}
= {f, 3}

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Ex 1.4, 10
If X = {a, b, c, d} and Y = ff, b, d, g}, find
(iii) X NY
XY = {a, b, c, d} / ff, b, d, g}
= {b, d}

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Ex 1.4, 11
If R is the set of real numbers and Q is the set of rational
numbers, then what is R— Q?
Real numbers

Rational numbers __ Irrational numbers

R: set of real numbers

Q: set of rational numbers
Therefore, R-—Q = Set of irrational numbers.

Ex 1.4, 12 teachoo.com
State whether each of the following statement is true or false. Justify
your answer.
(i) (2, 3, 4, 5} and {3, 6} are disjoint sets.
{2, 3, 4, 5} {3, 6} Two sets are disjoint if they have no

= {3} common element

+0 /n Intersection— Common of two sets

If \ 0 B=Q, then sets are disjoint

Since, there is a commen element in both set.
The given sets are not disjoint.
So, the given statement is False

teachoo

Ex1.5,1
Let U = {1, 2, 3, 4,5, 6, 7, 8, 9},
A= {1, 2, 3, 4},
B= {2, 4, 6, 8} and
C= {3, 4, 5, 6}. Find
(i) A’
N=U-A

= {1, 2, 3, 4,5, 6, 7,8, 9}— {1, 2,3, 4}

= {5, 6, 7, 8, 9}

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

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

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

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

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

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Ex 1.5, 2
If U = {a, b, c, d, e, f, g, h}, find the complements of following sets:
(i) A = {a, b, c}
AN =U-A
= {a, b, c,d, e, f, g, h}— {a, b, c}
= {d, e, f, g, h}

teackoo.co:
Ex 1.5, 3 “
Taking the set of natural numbers as the universal set, write down
the complements of the following sets:
(i) {x: x is an even natural number}
Natural numbers
Odd numbers Even numbers
Universal set is the set of natural numbers
{x: x is an even natural number}’
= {x: x is an odd natural number}

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

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

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

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

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

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

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

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

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

Taking the set of natural numbers as the universal set, write down the complements of the following sets:
(xi) {x: x ∈ N and 2x + 1 > 10}

Ex 1.5, 4 teachoo.com
If U = {1, 2, 3, 4, 5, 6, 7, 8, 9},
A= {2, 4, 6, 8} and B = {2, 3, 5, 7}, verify that
U Union - Combination of two sets
AUB AN =U-A
= {2, 4, 6, 8} U {2, 3, 5, 7} = {1, 2,3, 4,5, 6, 7, 8, 9}-{2,4,6,8
= {2, 3, 4,5, 6, 7, 8} = {1, 3, 5, 7, 9}
(AU By’ B’=U-B
=U- (AUB) = {1, 2, 3, 4,5, 6, 7, 8, 9}—- {2, 3,5, 7
= {1, 2, 3, 4,5, 6, 7,8, 9} = {1 4, 6, 8, 9}
— {2, 3, 4, 5, 6, 7, 8} NAB’
= {1,9} = {1, 3, 5,7, 9} {1, 4, 6, 8, 9}
= {1, 9}

teachoo.com
Ex 1.5,5
Draw appropriate Venn diagram for each of the following:
(i) (AU BY’
Step 1
Draw U, A&B
Step 2
MarkAUB

Ex 1.5, 6 teachoo.com
Let U be the set of all triangles in a plane. If Ais the set of all triangles
with at least one angle different from 60°, what is A’?
U = Set of all triangles in a plane
A = Set of all triangles with at least one angle different from 60 °
A’ = Set of all triangles with no angle different from 60°
= Set of all triangles with all three angles 60°
(As, in an equilateral triangle, all angles are 60° )
= Set of all equilateral triangles

teachoo.com
Ex 1.5, 7
Fill in the blanks to make each of the following a true statement:
(i) AUN =...
AUN

Example 1 teachoo
Write the solution set of the equation x? + x — 2 = 0 in roster form.
Solving the given equation

x*+x-2=0

+ 2x—-x-2=0

x(x+ 2)-1(x+2)=0

(x-1) (x+2)=0
So,x=1,-2
Therefore, the solution set of the given equation can be written in
roster form as

{1, -2}

teachoo.com

Example 2
Write the set {x : x is a positive integer and x? < 40} in the roster
form.
Positive integer = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10...

=1

2=4

3=9

42=16

57=25

6? = 36

—#P=49— >40

The required numbers are 1, 2, 3, 4, 5, 6.

teachoo.

Example 3 ‘eachoo.com
Write the set A = {1, 4, 9, 16, 25,... } in set-builder form.
A={1, 4,9, 16, 25,...}
A={1?, 2’, 37, 47, 57,...}
Here,
1, 2, 3, 4, 5 are all natural numbers
and 1, 4, 9, 16, 25 are their squares
Hence, we may write the set A as

A= {x : xis the square of a natural number}

or
A={x:x=n’, where n € N}

teackoo.com
Example 4
. 2 3 5 6). .
Write the set Ei aot _ => s} in the set-builder form.
2'3'4'5’6'7

Each member in the given set has
denominator 1 more than numerator
Also, the numerator begins from 1

and does not exceed 6.
Hence, in the set-builder form the given set is

{x x= =. Where nis a natural number and 1<ns 6}

Example 5 teackoo.com
Match each of the set on the left described in the roster form with
the same set on the right described in the set-builder form :

(i) {P, R, 1, N, C, A, L} (a) {x sis a positive integer and is a divisor of 18}
(ii) {0} / dissemi nt -9°0)

(iii) {1, 2, 3, 6, 9, 18} (c) {x : x is an integer and x + 1= 1}

(iv) {3, -3} (d) (x : xis a letter of the word PRINCIPAL}
{x: xis a positive integer and is a divisor of 18}

1, 2,3, 6, 9, 18 are all divisors of 18

So, (iii) matches (a).

teachoo.com
Example 6
State which of the following sets are finite or infinite
(i) {x x © N and (x— 1} (x-2) = 0}
(x- 1) (k-2)=0
wX= 1,2
Given set = {1, 2}.
Since the set has 2 elements (countable).
Hence, it is finite.

Example 6
State which of the following sets are finite or infinite
(ii) {x : x ∈ N and x2 = 4}

Example 6
State which of the following sets are finite or infinite
(iii) {x : x ∈ N and 2x –1 = 0}

Example 6
State which of the following sets are finite or infinite :
(iv) {x : x ∈ N and x is prime}

Example 6
State which of the following sets are finite or infinite :
(v) {x : x ∈ N and x is odd}

Example 7 teackoo.com
Find the pairs of equal sets, if any, give reasons:
A= {0}, B={x:x>15 andx <5},
C={k:x-5=0}, D={x:x?=25},
E = {x : xis an integral positive root of the equation x* — 2x —15 = 0}.
Let’s write all the sets in roster form
A= {0}
A= {0}
B={x:x>15 and x < 5},
No number can be greater than 15 and less than 5 simultaneously.
B={}=0

Example 8 teachoo.com
Which of the following pairs of sets are equal? Justify your answer.
(i) X, the set of letters in “ALLOY” and B, the set of letters in “LOYAL”.
X={A,L,L, O, Y}, but Lis repeated.

So, X = {A, L, O, Y}
B={L, O, Y, A, L}. but Lis repeated.

So, B = {0, Y, A, L}
Elements of set A=A, L, 0, Y
Elements of set B = O, Y, A, L
Every element of X is same as every element of B.
~X=B

Example 8
Which of the following pairs of sets are equal? Justify your answer.
(ii) A = {n : n ∈ Z and n2 ≤ 4} and B = {x : x ∈ R and x2 – 3x + 2 = 0}.

teackoo.

Example 9 eackhoo.com
Consider the sets b, A= {1, 3}, B= {1, 5, 9}, C= {1, 3, 5, 7, 9}.
Insert the symbol C or ¢ between each of the following pair of sets:
(i) >...B

Cc - isa subset

¢ - is not a subset
Null set is a subset of every set
So, o is a subset of every set.
“ PCB

Example 10 teackoo.com
Let A={a,e, i, 0, uy} & B= {a, b, c, d}. Is Aa subset of B? No. (Why?).
Is Ba subset of A? No. (Why?)

A= {a, e, i, 0, u}

B = {a, b, c, d}

(i) Ils AC B?

For a set to be sub set of another set, it needs to have all elements
present in the another set.

In set A {e, i, o, u} elements are present but these are not in present
in set B.

Hence A ¢ B

feackoo.
Example 11 PAEHOO.LOWN
Let A, B and C be three sets. If AG Band BCC, is it true that A C C?.
If not, give an example.
Given: A, B, C are three sets
AE€BandBcA

To show: A C C or not?
Proof: We will prove this with the help of an example.
Let A= {1}

B= {{1}, 2, 3}

C = {{1}, 2, 3, 4, 5}

teackoo.com
Example 12
Let A={ 2, 4, 6, 8} and B ={6, 8, 10, 12}. FindA UB.
U Union - Combination of two sets
AUB=(2, 4,6, 8} U {6, 8, 10, 12}
Common elements 6, 8 should be taken once
= {2, 4, 6, 8, 10, 12}

teackoo.com

Example 13
Let A={a,e,i,0, uu} and B={a,i,u}. Showthat AUB=A
U Union - Combination of two sets
A={a,e,i,0,u}
B = {a, i, u}
AUB={a,e,i,0,u}U fa, i, u}

={a,e,i,0,u}

=A
Hence proved

Example 14 teackoo.com
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 the school football team.
Find X U Y and interpret the set.
U Union - Combination of two sets

Given X = {Ram, Geeta , Akbar}

Y = {Geeta, David, Ashok}
Common elements (Geeta) should be taken once
X UY = {Ram, Geeta, Akbar, David, Ashok}.
This is the set of students from Class XI who are in the hockey
team or the football team or both.

teachoo.com
Example 15
A=(2,4,6, 8} and B={6, 8, 10, 12}. Find An B.
M Intersection — Common of two sets
A B= {2, 4, 6, 8} M (6, 8, 10, 12}
6, 8 are the only elements which are common to both A and B.
= {6, 8}

teachoo.com
Example 16
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 the school football team. Find
XY.
XM Y= {Ram, Geeta, Akbar} N {Geeta, David, Ashok}
Element ‘Geeta’ is the only element common to both.

= {Geeta}.

teachoo.com
Example 17
Let A= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and B = { 2, 3, 5, 7}.
Find AN B and hence show that AN B=B.
/N Intersection — Common of two sets

AN B={1, 2, 3, 4,5, 6, 7, 8, 9, 10} N { 2, 3, 5, 7}

={2,3,5,7}

=B.
Hence proved

Example 18 teachoo.com
LetA={1, 2,3, 4,5, 6}, B={2,4, 6,8}. Find A~B and B—A.
A-B=A-(ANB) A-B=A-(ANB)
fn Intersection — Common of two sets

An B= {1, 2, 3, 4, 5, 6} N {2, 4, 6, 8}

= {2, 4, 6}
A-B=A-(ANB)

= {1, 2, 3, 4, 5, 6} {2, 4, 6}

={1, 3, 5}
B-A=B-(BNA)

=B-(ANB)

= {2, 4, 6, 8 }— {2, 4, 6}

= {8}

teachoo.
Example 19 PAEHOO.LOWN
Let V={a,e,i, 0, u} and B= {a,i,k, u}. Find V-B andB-V
A-B=A-(ANB)
V-B=V-(VnB)
fn Intersection — Common of two sets
VN B= fa, e, i, 0, U} M {a, i, k, u}
= fa, i, u}
V-B=V-(VNB)
= {a, e, i, 0, u }— {a, i, u}
= {e, o}
B-V=B-(BNV)
=B-(VNB)
= {a, i, k, u}—{a, i, u}
= {k}

teachoo.com
Example 20
Let U = {1, 2, 3, 4,5, 6, 7, 8, 9, 10}. and A = {1, 3, 5, 7,9}. Find A’.
A’=U-A
= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} — {1, 3, 5, 7,9}
= {2, 4, 6, 8, 10}

teachoo.com

Example 21
Let U be universal set of all the students of Class XI of a
coeducational school and A be the set of all girls in Class XI. Find A’.
In a coeducational school, there can be only boys and girls in a
school.
Ais the set of all girls,

A’ = Set of all Students — Set of all girls

A’ = Set of all boys in class XI.

Example 22 teackoo.com
Let U = {1, 2, 3, 4, 5, 6}, A= {2, 3} and B = {3, 4, 5}.
Find A’, B’, A’ B’, AU B and hence show that (A U B)’=A’ NB’.
A’=U-A
N Intersection — Common of two sets
= {1, 2, 3, 4, 5, 6}— {2, 3} oo
U Union - Combination of two sets
= {1, 4, 5, 6}
B’=U-B
= {1, 2, 3, 4, 5, 6}— {3, 4, 5}
= {1, 2, 6}
Now,
A’ NB’
= {1, 4,5, 6} 9 {1, 2, 6}
= {1, 6}

teachoo.com

Example 23
Show that the set of letters needed to spell “ CATARACT” and
the set of letters needed to spell “ TRACT” are equal.
Let X be the set of letter in “CATARACT”.
“X={C,A,T,R} (1)
Let Y be the set of letter in “TRACT”.
“Y={T,R,A,C} ...(2)
Since every element of X and Y are equal

Hence, X=Y¥

Example 24 teachoo.com
List all the subsets of the set {-1, 0, 1}.
Let A= {-1, 0, 1}
Number of elements in A is 3
Hence, n= 3
Number of subsets of A= 2"
where n is the number of elements of the set A
=2? =8
The subsets of {-1, 0, 1} are
®,
and {-1, 0, 1}

teachoo.com
Example 25
Show that AU B =An B implies A= B
In order to prove A= B, we should prove
° Ais asubset of Bie. ACB
* &Bisasubset of Aie.B CA
Let x EA.
Then, x € AUB.
Since A UB=ANB,
~ XEANB.
So, x € B.

Example 23 teackoo.com
If X and Y are two sets such that X U Y has 50 elements, X has 28
elements & Y has 32 elements, how many elements does X N Y have ?
n (XU Y)=50,
n (X) = 28,
n (Y) = 32,
n(XN Y=?
By using the formula

n(XUY)=n(X)tn(Y)-n(xXnY},

50 = 28+ 32-n(XUY)

n(XUY)=60-50

n(XUY)=10

Example 24 teachoo.com
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 ?
Let M denote the set of teachers who teach mathematics
and P denote the set of teachers who teach physics.
The word ‘or’ means union and the word ‘and’ means intersection.
Hence,
Number of teachers who teach Maths or Physics = n(M U P) = 20
Number of teachers who teach Maths = n(M}) = 12
Number of teachers who teach Maths and physics = n(M n P) = 4
Number of teachers who teach physics = n(P) = ?

Example 25 teackoo.com

Ina class of 35 students, 24 like to play cricket and 16 like to play

football. Also, each student likes to play at least one of the two

games. How many students like to play both cricket and football ?

Let C be the set of students who like to play cricket

& F be the set of students who like to play football.

Number of students who like to play cricket = n(C) = 24

Number of students who like to play football = n(F) = 16

Number of students who like to play atleast cricket and football
=n(C UF) =35

Number of students who like to play both cricket and football
=n(C Nn F)=?

Example 26 teackoo.com

In a survey of 400 students in a school,100 were listed as taking

apple juice, 150 as taking orange juice and 75 were listed as taking

both apple and orange juice. How many students were taking

neither apple juice nor orange juice.

Let A, O denote the set of students taking apple juice & orange

juice respectively,

Number of students who take apple juice = n(A) = 100

Number of students who take orange juice = n(O) = 150

Number of students who take both orange juice and apple juice
=n(O NA) =75

teackoo.
Example 27 PAEHOO.LOWN
There are 200 individuals with a skin disorder, 120 had been exposed
to the chemical C,, 50 to chemical C,, and 30 to both the chemicals
C, and C,. Find the number of individuals exposed to
(i) Chemical C, but not chemical C,
People exposed to chemical C,
People exposed to only People exposed to both
chemical C, chemical C, &C,
Number of people exposed to chemical C, but not Chemical C,
= Number of people exposed to chemical C,
— Number of people exposed to both chemical C, & C,

Example 31 teackoo.com
For any sets A and B, show that P(A B) = P(A) © P(B).
To prove two sets equal,
we need to prove that they are subset of each other i.e..
we have to prove C Subset
© P(AN B) CP(A) P(B) |ACB (all elements of set A in set B)
© & P(A) NO P(B) CP (ANB)
Let a set X belong to Power set P(A © B)
ne.XEP(ANB).
As set X is in the power set of AN B, X is a subset of AN B because
power set is the set of all subsets

teackoo.
Example 32 PAEHOO.LOWN
A market research group conducted a survey of 1000 consumers
and reported that 720 consumers like product A and 450
consumers like product B, what is the least number that must have
liked both products?
Let set of consumers who liked the product A & product Bbe A&B
respectively
Number of consumers who liked product A = n(A) = 720,
Number of consumers who liked product B = n(B) = 450
We know that

n(A UB) =n (A) +n (B)—n (ANB)

teackoo.com

Example 33
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?
Let the set of owners of car A & car B be A & B respectively
Number of car A owned = n{A) = 400
Number of car B owned = n(B) = 200
Number of car A and car B owned = n(A © B) = 50
We know that
n{A U B)=n (A) +n(B)—n (ANB)

= 200 + 400-50

= 550

Example 34 teackoo.com

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 3

men got medals in all the three sports, how many received

medals in exactly two of the three sports ?

Let F , B, C denote the set of people who received medals in

football , basketball & cricket respectively

Number of medals won in football = n(F) = 38,

Number of medals won in basketball = n (B) = 15,

Number of medals won in cricket = n (C) = 20

Number of medals won in either football,basketball or cricket
=n(FUBUC)=58

Misc 1 teachoo
Decide, among the following sets, which sets are subsets of one
and another:
A= {x: x € R and x satisfy x? — 8x + 12 = 0}, B = {2, 4, 6},
C={2, 4, 6, 8...}, D = {6}.
A={x:x € R and x satisfies x? — 8x + 12 = 0}
Solving x? — 8x +12 =0
x? — 6x -2x +12 =0
x (x— 6) -2(x- 6) =0
x=2,6
“A= {2,6}
Thus, A ={2, 6}, B = {2, 4, 6}, C={2, 4,6, 8...}, D= {6}

Misc 2 teackoo.com
In each of the following, determine whether the statement is true or
false. If it is true, prove it. If it is false, give an example .
(i) Ifx EA andAEB, thenx EB
Let A= {1, 2} C-is a subset
Since Lis an element of set, |4 © 8 fall elements of A are in B
€ - (belongs to) element in set
Let x=1,1€ {1,2}.
Also, A € B, i.e. whole set A is an element of set B
Taking B = { {1, 2}, 3,4,5}
We have to prove that
xEB

Misc 2
In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an Example
(ii) If A ⊂ B and B ∈ C, then A ∈ C

Introduction (Example)
In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an Example .
(iii) If A ⊂ B and B ⊂ C, then A ⊂ C

Misc 2
In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example .
(iv) If A ⊄ B and B ⊄ C, then A ⊄ C

Misc 2
In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example .
(v) If x ∈ A and A ⊄ B, then x ∈ B

Introduction(Example)
In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example .
(vi) If A ⊂ B and x ∉ B, then x ∉ A

teachoo.com
Misc 3
Let A, B and C be the sets such thatA UB=AUCandAnN B=ANC.
show that B=C.
In order to prove B = C, we should prove
Bis a subset of Cie. B OC
& Cis a subset of Bi.e.C CB
Letx€B (1)
> xEAUB (SinceB C AUB, all elements of Bare in A UB)
=>xEAUC (GivenAUB= AUC)
>xeEAorxEec (2)

Misc 4 teachoo.com
Show that the following four conditions are equivalent:
(JACB (ii) A- B=
(iii) AUB=B (iv) AN B=A | C-isa subset
AC Bifall elements of Aare in §

Showing Condition (i) is equivalent to Condition (ii).

LetACB U

This means all elements of A are in B,

So, A has no element different from B

>A-B=0
Showing Condition (ii) is equivalent to Condition (iti).

A-B=@

This means A has no elements different from B

So, all elements of A are in B

So, AUB=B

teackoo.com
Misc 5 - Introduction
Show that if AC B, then C-BCC-A.
C - is a subset

Let AC Bif all elements of Aare in B
A={1, 2}, B= {1, 2, 3}, C= {1, 2, 3, 4}
C-B={1, 2, 3, 4}— {1, 2, 3}

= {4}
C-A={1, 2, 3, 4}- {1, 2}

= {3, 4}
{4} < {3, 4}
So,C-BC C-A

teachoo.com
Misc 6 - Introduction
Show that for any sets A and B,
A=(AN B) U(A-B) and AU (B—A)=(A UB)
Let U = {1, 2, 3, 4, 5} Also
A={1, 2} B’=U-B
B= {2, 3,4} = {1, 2, 3, 4, 5}— {2, 3, 4}
= {1, 5}

A-B=A-(ANB) A-B=AnB’

= {1, 2}- {2} ={1, 2} 9 {1, 5}

={1} = {1}
We use the result A— B = A 1 B’ in this question

teachoo.com
Misc 7
Using properties of sets show that
(i) AU (AN B)=A U Union - Combination of two sets
fn Intersection — Common of two sets

In order to prove AU (AN B)=A,
we should prove

AU (ANB) is asubset of Ai.e. AU(ANB) CA

& Ais a subset of AU (AMB) i.e. A CAU (ANB)

As set is a subset of itself, ACA
Also, Ais asubsetof AN B,ie.ACANB

as all elements of set A are inANB

teachoo.com

Misc 8
Show that An B= AN Cneed not imply B= C.
We have to prove false, so we take a example
It is given that AN B=ANC
i.e. Common element in set A & B= Common element in set A&C
Let

A = {0, 1},

B = {0, 2, 3},
and C= {0, 4,5}

Mise 9 teachoo.com
Let A and B be sets. IfANX=BNX=@andAU X=B UX for
some set X, show that A = B.
(Hints: A= An (AU X), B =B 9 (BU X) and use distributive law)
Given: Let A and B be two sets such that
ANX=BOX=@ andAUX=B UX for some set X.
To prove: A=B
Proof:
Let A=AN(AUX)
A=An (BUX) (Given AUX =BUX)

teachoo.com

Misc 10
Find sets A, B and Csuchthat An B,BO CandAn Care non-
empty sets and AN BN C=@.
AB should be non-empty,

ie. there should be some common element between A & B
Similarly,
Bn Cshould be non-empty,

ie. there should be some common element between B & C
AC should be non-empty,

ie. there should be some common element between A & C

Misc 6 teachoo.com
Assume that P (A) = P (B). Show that A = B.
in order to prove A = B, we should prove
Ais a subset of Bie. A CB C Subset
& Bisa subset of Ai.e.B CA AcB .
(All elements of set A in set B}
Set A is an element of power set of A as every set is a subset
(Eg: for set A = {0, 1}, P(A) ={@, {0}, {1}, {0, 1} } So, Ais in P(A))
ie. A € P(A)
=> AE P(B) (Since P(A) = P(B))
If set A is in power set of B,
set A is a subset of B
“ACB

Misc 7 teackoo.com
Is it true that for any sets A and B, P (A) U P (B) = P (A U B)? Justify
your answer.
(if it is false, we take an example to prove it)
Let A = {0, 1} and B = {1, 2}
P(A) = {@ , {0}, {2}, {0, 1}}
AU B={0, 1, 2} P(B) = {@, {1}, {2}, (1, 2H
P(A) U P(B} =
PIA UB) = {9 {@, {0}, {1}, {0, 13, (21, 11, 21)
{O}, {1}, {2},
{0, 1}, {1, 2}, {0, 2},
{0, 1, 2} }
-. P(A) U P(B) # P(A U B)
So, the given statement is False

Misc 13 teachoo.com
In a survey of 600 students in a school, 150 students were found to
be taking tea and 225 taking coffee, 100 were taking both tea and
coffee. Find how many students were taking neither tea nor coffee?
Let T, C be the set of students taking tea & coffee respectively
Number of students taking tea = n(T) = 150
Number of students taking coffee = n(C) = 225
Number of students taking both tea and coffee = n(T © C) = 100
n{T U C) = n(T) +n(C)—n(T 9 C)]

= 150+ 225-100

=275
Number of students taking either tea or coffee = n(T U C} = 275

teachoo.com
Misc 14
In a group of students 100 students know Hindi, 50 know English
and 25 know both. Each of the students knows either Hindi or
English. How many students are there in the group?
Let E be the set of all students who know English.
and H be the set of all students who know Hindi.
Number of students who know Hindi = n(H) = 100
Number of students who know English = n(E} = 50
Number of students who know both Hindi and English = n(H m E)
=25
Since, each of the students know Hindi or English

Misc 15 teachoo.com
In a survey of 60 people, it was found that 25 people read
newspaper H, 26 read newspaper T, 26 read newspaper |, 9 read
both H and 1,11 read both H and T, 8 read both T and |, 3 read all
three newspapers. Find:

(i) the number of people who read at least one of the newspapers.
Number of people who read newspaper H = n(H) = 25,

Number of people who read newspaper T = n(T) = 26,

Number of people who read newspaper | = n(I) = 26,

Number of people who read both H & | = n(H 9 I) =9,

Number of people who read both H & T=n(HMT)= 11

Number of people who read both T &l=n(T 9 I) = 8

Number of people who read all H T&l=n(HNTOI= 3

Misc 16 teachoo.com
In a survey it was found that 21 people liked product A, 26 liked
product B & 29 liked product C. If 14 people liked products A & B,
12 people liked products C & A, 14 people liked products B & C and
8 liked all the three products. Find how many liked product C only.
Let A, B, C be the set of people who like product A, product B &
product C respectively

Number of people who liked product A = n(A)= 21,

Number of people who liked product B = n(B)= 26,

Number of people who liked product C = n(C) = 29,

Number of people who liked product A and B = n{A Nn B} = 14,
Number of people who liked product C and A= n(C m A) = 12,

teachoo

Ex 1.6, 1
If X and Y are two sets such that n(X) = 17, n(Y) = 23 and n (XU Y)
= 38, find n(X n Y).
n(X) = 17, n(Y) = 23, n(X U Y) = 38
n(X 9 Y)=?
We know that

n(X U Y) = n(X)+ n(Y)— n(X 9 Y)

38 = 17+ 23-n(X NY)

38 = 40-—n(Xn Y)

n(X n Y) = 40-38

n(X n Y)= 2

Ex 1.6, 2 teachoo.com
If X and Y are two sets such that X U Y has 18 elements, X has
8 elements and Y has 15 elements; how many elements does
X NY have?
Given, n(X U Y) = 18,
n(X) = 8,
n(Y)=15
n(Xn Y)=?
We know that:
n(X U Y) = n(X) + n{Y} - n(X 9 Y)
18 =8+15 —n(XnY)
18 = 23 —n(Xn Y)
n(X 0 Y)= 23-18
n(X NY) =5

teachoo.com
Ex 1.6, 3
In a group of 400 people, 250 can speak Hindi and 200 can speak
English. How many people can speak both Hindi and English?
Let H be the set of people who speak Hindi,
and E be the set of people who speak English
Number of people who speak Hindi = n(H) = 250
Number of people who speak English = n(E} = 200
Total number of people = n(H U E) = 400
Number of people who can speak both English and Hindi = n(H © E)
=?
Now,
n({H U E) = n(H) + n(E) — n(H 9 E)
400 = 250 + 200 — n(H 0 E)

teackoo.com
Ex 1.6, 4
If S and T are two sets such that S has 21 elements, T has 32
elements, and SN T has 11 elements, how many elements does $
UT have?
n(S) = 21, n(T) = 32, n(S NT) =11
We know that:
n{(SUT)=n(S)+n(T)—n (SOT)
vn (SUT)=21432-11=42
Thus, the set (S U T) has 42 elements.

Ex 1.6,5 teachoo.com
If X and Y are two sets such that X has 40 elements, X U Y has 60
elements and XN Y has 10 elements, how many elements does Y have?
Given n(X) = 40, n(X U Y) = 60, n(X m Y) = 10
We know that:
n(X U Y) = n(X) + n(Y) — n(X 2 Y)

60 = 40 + n(Y)—10

60 = 40-10 + n(Y)

60 = 30 + n{Y}

« n{Y) = 60 — (30)
n{Y) = 30

Thus, the set Y has 30 elements.

teachoo.com
Ex 1.6, 6
In a group of 70 people, 37 like coffee, 52 like tea, and each
person likes at least one of the two drinks. How many people like
both coffee and tea?
Let C denote the set of people who like coffee, and
T denote the set of people who like tea
Number of people who like coffee = n(C) = 37
Number of people who like tea= n(T) = 52
Number of people who like at least tea or coffee = n(C U T) = 70
Number of people who like both tea & coffee = n(C N T)=?

teachoo.com

Ex 1.6, 7
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?
Let C & T denote the set of people who like cricket & tennis resp.
Number of people in the group

= Number of people who like cricket or tennis

=n{C UT) =65,
Number of people who like cricket = n(C) = 40,
Number of people who like both cricket and tennis = n(C N T} = 10

Ex 1.6, 8 teachoo.com
In a committee, 50 people speak French, 20 speak Spanish and

10 speak both Spanish and French. How many speak at least

one of these two languages?

Let F be the set of people in the committee who speak French,

and S be the set of people in the committee who speak Spanish
Number of people who speak French = n(F) = 50,

Number of people who speak Spanish = n{S} = 20,

Number of people who speak French & Spanish = n(§ 9 F) = 10
People who speak atleast on of the language = n(S U F)

Chapter 1 Class 11
Sets
- MCQ Worksheet 1
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Chapter 1 Class 11 - Sets
- Mix Questions Worksheet 1
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Chapter 1 Class 11 - Sets
- Assertion and Reasoning
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Chapter 1 Class 11 Sets
- Case Based Question
Worksheet 1
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