Class 11 Maths Chapter 1 Sets Exercise 1.4 Solutions in English Medium
Free NCERT Solutions for
Class 11 Maths Chapter 1 Exercise 1.4 prepared by expert Mathematics teacher as
per CBSE (NCERT) books guidelines.
Free NCERT Solutions for Class 11 Math’s Chapter 1 Sets Exercise 1.1, Exercise 1.2, Exercise 1.3, Exercise 1.4, Exercise 1.5, Exercise 1.6 and Miscellaneous Exercise in English Medium for CBSE.
NCERT Maths Class 11 Sets. Just click on the Exercise wise links given below to practice the Maths solutions for the respective exercise.
| SETS | Solutions Link |
|---|---|
| Exercise 1.1 | Click here |
| Exercise 1.2 | Click here |
| Exercise 1.3 | Click here |
| Exercise 1.4 | Click here |
| Exercise 1.5 | Click here |
| Exercise 1.6 | Click here |
Class 11 Maths Chapter 1
Sets Ex 1.4 Questions with Solutions to help you to revise complete Syllabus
and Score More marks in your exams.
EXERCISE 1.4
1.
Find the union of each of the following pairs of sets
:
(i)
X = { 1, 3, 5 } Y = { 1, 2, 3 }
(ii)
A = [ a, e, I, o, u } B = { a, b, c }
(iii)
A = { x : x is a natural number and
multiple of 3 }
B = { x : x is a natural number less than 6
}
(iv)
A = { x : x is a natural number and 1
< x ≤ 6 }
B = { x : x is a natural number and 6 <
x < 10 }
(v)
A = { 1, 2, 3 } , B = ϕ
Solution:-
(i)
Given,
X
= { 1, 3, 5 } Y = { 1, 2, 3 }
X ∪ Y
= { 1, 2, 3, 5 }
(ii)
Given,
A = [ a, e, I, o, u } B = { a, b, c }
A ∪ B = { a, b, c, e, I, o, u }
(iii) Given,
A = { x : x is a natural number and multiple of 3 } B = { x : x is a natural number less than 6 }
So the union of pairs of
set can be written as
A
∪ B = { 1, 2, 4, 5, 3, 6, 9, 12 …… }
(iv) Given,
A = { x : x is a natural number and 1 < x ≤ 6 }
B = { x : x is a natural number and 6 < x < 10 }
So the union of pairs of
set can be written as
A
∪ B = { 2, 3, 4, 5, 6, 7, 8, 9 }
(v) Given,
A = { 1, 2, 3 } , B = ϕ
A ∪ B = { 1, 2, 3,4 }
2. Let A = { a, b }, B
= { a, b, c } . Is A ⊂ B ? What is A ∪ B ?
Solution:-
Here, A = { a, b } and B =
{ x, y, z }
Yes , A ⊂ B.
A ∪ B = { a, b, c } = B
3. If A and B are two sets such that A ⊂ B, then what is A ∪ B
?
Solution:-
If A and B are two sets
such that A ⊂ B, then A ∪ B = B
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)
A ∪ B
(ii)
A ∪ C
(iii)
B ∪ C
(iv)
B ∪ D
(v)
A ∪ B ∪ C
(vi)
A ∪ B ∪ D
(vii)
B ∪ C ∪ D
Solution:-
A = { 1, 2, 3, 4 }, B = {
3, 4, 5, 6 }, C = { 5, 6, 7, 8 } and D =
{ 7, 8, 9, 10 }
(i)
A ∪ B = { 1, 2, 3, 4, 5, 6 }
(ii)
A ∪
C = { 1, 2, 3, 4, 5, 6, 7, 8 }
(iii)
B ∪ C = { 3, 4, 5, 6, 7, 8 }
(iv)
B ∪ D = {3, 4, 5, 6, 7, 8, 9, 10 }
(v)
A ∪ B ∪ C = { 1, 2, 3, 4, 5, 6, 7, 8 }
(vi)
A ∪ B ∪ D = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
}
(vii)
B ∪ C ∪ D = { 3, 4, 5, 6, 7, 8, 9, 10 }
5. Find the intersection of each pair of sets of question 1
above .
Solution:-
(i)
X ∩ Y
= { 1, 3, 5 } ∩ { 1, 2, 3 } = {
1,3 }
(ii)
A ∩ B = [ a, e, i, o, u } ∩ { a,
b, c } = { a }
(iii)
A = { 3, 6, 9, 12, . . . . .}
B = { 1, 2, 3, 4, 5 }
A ∩ B { 3, 6, 9, 12, . . . . .} ∩ { 1,
2, 3, 4, 5 } = { 3 }
(iv)
A = { 2, 3, 4, 5, 6 }
B = { 7, 8, 9 }
A ∩ B = { 2, 3, 4, 5, 6 } ∩ { 7, 8, 9 } = ϕ
(v)
A = { 1, 2, 3 } ∩ B =
ϕ = ϕ
6.
If A = { 3, 5, 7, 9, 11 } ,
B = { 7, 9, 11, 13 }, C = { 11, 13, 15 } and D = { 15, 17 }; find
(i)
A ∩ B
(ii)
B ∩ C
(iii)
A ∩ C
∩ D
(iv)
A
∩ C
(v)
B ∩ D
(vi)
A ∩ (B
∪ C )
(vii)
A
∩ D
(viii)
A ∩ (B ∪ D )
(ix)
( A ∩ B ) ∩ ( B ∪ C )
(x)
( A ∪ D ) ∩ (B ∪ C )
Solution:-
(i)
A ∩ B = { 7, 9, 11 }
(ii)
B ∩ C = { 11, 13 }
(iii)
A ∩ C
∩ D = { A ∩ C } ∩ D = {11 } ∩ { 15, 17 } = ϕ
(iv)
A ∩ C = {11 }
(v)
B ∩ D = ϕ
(vi)
A ∩ (B
∪ C ) = ( A ∩ B ) ∪ = ( A ∩ C ) = { 7, 9, 11 } ∪ {
11 } = { 7, 9, 11 }
(vii)
A
∩ D = ϕ
(viii)
A ∩ (B ∪ D ) = ( A ∩ B ) ∪ (A ∩ D) = { 7, 9, 11 } ∪ ϕ = { 7, 9, 11 }
(ix)
( A ∩ B ) ∩ ( B ∪ C ) = { 7, 9, 11
} ∩
{ 7, 9, 11, 13, 15 } = { 7, 9, 11 }
(x)
( A ∪ D ) ∩ (B ∪ C ) = { 3, 5, 7, 9,
11, 15, 17 ) ∩ { 7, 9, 11, 13, 15 } = { 7, 9, 11, 15 }
7.
If A = { x : x is a natural number }, B = { x : x is a even natural number } C = { x : x is an odd natural } and D = { x : x is a prime number } , find
(i)
A ∩ B
(ii)
A ∩ C
(iii)
A ∩ D
(iv)
B ∩ C
(v)
B ∩ D
(vi)
C
∩ D
Solution:-
A = { x : x is a natural number} = { 1, 2, 3,
4, 5 …. }
B = { x : x is a even
natural number } = { 2, 4, 6, 8 }
C = { x : x is an odd
natural } = { 1, 3, 5, 7, 9 }
D = { x : x is a prime
number } = { 2, 3, 5, 7 … … .}
(i)
A ∩ B
= { x : x is a even natural number } = B
(ii)
A ∩ C = { x : x is an odd natural } = C
(iii)
A ∩ D = { x : x is a prime number } = D
(iv)
B ∩ C = ϕ
(v)
B ∩ D = { 2 }
(vi)
C
∩ D = { x : x is an odd natural
}
8.
Which of the following pairs of are disjoint
(i)
{ 1, 2, 3, 4 } and { x : x is a
natural number and 4 ≤ x ≤ 6 }
(ii)
{ a, e, i, o, u } and { c, d, e, f }
(iii)
{ x : x is an even integer } and { x : x is an odd integer }
Solution:-
(i)
{ 1, 2, 3, 4 }
{ x : x is a natural number and 4 ≤ x ≤ 6 }
= { 4, 5, 6 }
Now, { 1,2, 3, 4 } ∩ { 4, 5, 6 } = { 4 }
Therefore, this pair of
sets is not disjoint .
(ii)
{ a, e, i, o, u } ∩ { c,
d, e, f } = { e }
Therefore, this pair of
sets is not disjoint .
(iii)
{ x : x is an even integer } ∩ { x : x is an odd integer } = ϕ
Therefore, this pair of
sets is disjoint .
9.
If A = { 3, 6, 9, 12, 15, 18, 21 }, B = { 4, 8, 12, 16, 20
} , B = { 4, 8, 12, 16, 20 }, C = { 2,
4, 6, 8, 10, 12, 14, 16 }, D = { 5, 10, 15, 20 }; find
(i)
A – B
(ii)
A – C
(iii)
A – D
(iv)
B – A
(v)
C – A
(vi)
D – A
(vii)
B – C
(viii)
B – D
(ix)
C – B
(x)
D – B
(xi)
C – D
(xii)
D – C
Solution:-
(i)
A – B
= { 3, 6, 9, 15, 18, 21 }
(ii)
A – C
= { 3, 9, 15, 18, 21}
(iii)
A – D
= { 3, 6, 9, 12, 18, 21 }
(iv)
B – A
= { 4, 8, 16, 20 }
(v)
C – A
= { 2, 4, 8, 10, 14, 16 }
(vi)
D – A
= { 5, 10, 20 }
(vii)
B – C
= { 20 }
(viii)
B – D
= { 4, 8, 12, 16 }
(ix)
C – B
= { 2, 6, 10, 14 }
(x)
D – B
= { 5, 10, 15 }
(xi)
C – D
= { 2, 4, 6, 8, 12, 14, 16 }
(xii)
D – C = { 5, 15, 20 }
10.
If X = { a, b, c, d } and
Y = { f, b, d, g }, find
(i)
X – Y
(ii)
Y – X
(iii)
X ∩ Y
Solution:-
(i)
X – Y = { a, c }
(ii)
Y – X = { f, g }
(iii)
X ∩ Y
= { b, d }
11.
If R is the set of real numbers and Q is the
set of rational numbers, then what is R – Q ?
Solution:-
R : set of real numbers
Q : set of rational
numbers
Therefore, R – Q is a set
of rational numbers
12.
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.
(ii)
{ a, e, I, o, u } and { a, b, c, d }
are disjoint sets.
(iii)
{ 2, 6, 10, 14 } and { 3, 7, 11, 15 }
are disjoint sets.
(iv)
{ 2, 6, 10 } and { 3, 7, 11 } are
disjoint sets.
Solution:-
(i)
False
As 3 ϵ { 2, 3, 4, 5 } , 3 ϵ
{ 3, 6 }
⇒ { 2, 3, 4, 5 } ∩ { 3, 6 } = { 3 }
(ii)
False
As a ϵ { a, e, i, o,
u} , a ϵ { a, b, c, d }
⇒ {a, e,
i, o, u } ∩ { a, b, c, d } = { a }
(iii)
True
As { 2, 6, 10, 14 } ∩ { 3,
7, 11, 15 } = ϕ
(iv)
True
As { 2, 6, 10 } ∩ { 3, 7,
11 } = ϕ
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