Class 11 Maths Chapter 1 Sets Exercise 1.5 Solutions in English Medium
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 |
EXERCISE : 1.5
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/ (ii) B/ (iii) ( A
∪ C )/ (iv) ( A ∪ B )/ (v) ( A/ )/ (vi) ( B – C )/
Solution:-
It
is given that,
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 } .
(i)
A/ = { 5, 6, 7, 8, 9 }
(ii)
B/
= { 1, 3, 5, 7, 9 }
(iii)
A ∪ C = {
1, 2, 3, 4, 5, 6 }
∴ (A ∪
C)/ = {7, 8, 9}
(iv)
A ∪ B = { 1, 2, 3, 4, 6, 8 }
So, we get
(A∪ B)/ = {5, 7, 9}
(v)
( A/ )/ = A = { 1, 2, 3, 4 }
(vi)
B
– C = {2, 8 }
So
we get
(B – C )/ = { 1, 3, 4, 5, 6, 7, 9 }
Exercise 1.5 Class 11 Maths Question 2
2. If U = { a, b, c, d, e, f, g, h }, find
the complements of the following sets :
(i)
A = {
a, b, c }
(ii)
B = {
d, e, f, g }
(iii)
C = {
a, c, e, g }
(iv)
D = {
f, g, h, a }
Solution:-
U
= {a, b, c, d, e, f, g, h}
(i) A =
{a, b, c}
A′={d,
e, f, g, h}
(ii) B =
{d, e, f, g}
∴B′={a,
b, c, h}
(iii) C =
{a, c, e, g}
∴C′={b,
d, f, h}
(iv) D =
{f, g, h, a}
∴D′={b,
c, d, e}
Exercise 1.5 Class 11 Maths Question 3
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 }
(ii)
{ x : x is an odd natural number }
(iii)
{ x :
x is n positive multiple of 3 }
(iv)
{ x :
x is a prime number }
(v)
{ x :
x is a natural number divisible by 3 and 5 }
(vi)
{ x :
x is a perfect square }
(vii)
{ x :
x is a perfect cube }
(viii)
{ x :
x + 5 = 8 }
(ix)
{ x :
2x + 5 = 9 }
(x)
{ x :
x ≥ 7 }
(xi)
{ x :
x
ϵ
N and 2x + 1 > 10 }
Solution:-
We know that,
U = N : set of Natural numbers
(i) Let A
= {x : x is an even natural number}
∴
A/ = U – A = U– {x : x is an
even natural number}
= {x : x is an odd natural number}
(ii) Let A
= {x : x is an odd natural number}
∴
A/ = U – A = U- {x : x is an odd natural number}
= {x : x is an even natural number}
(iii) Let A
= {x : x is a positive multiple of 3}
∴
A/ = U – A = U– {x : x is a
positive multiple of 3}
= {x : x is not a positive multiple of 3}
(iv) Let A
= {x : x is a prime number}
∴
A/ = U – A = U– {x : x is a prime number}
=
{x : x is not a prime number}
(v) Let A
= {x : x is a natural number divisible
by 3 and 5}
∴ A/ = U – A = U– {x : x is a
natural number divisible by 15}
=
{x : x is not divisible by 15}
(vi) Let A
= {x : x is a perfect square}
∴
A/ = U – A = U– {x : x is a perfect square}
=
{x : x is not a perfect square}
(vii) Let A
= {x : x is a perfect cube}
∴A/
= U – A = u– {x : x is a perfect cube}
=
{x : x is not a perfect cube}
(viii) Let A
= {x : x + 5 = 8} = {3}
To
find the complement of {x : x+5 = 8}
X
+ 5=8
X
=3
The
complement of set A is the set of all elements of U which are not the elements
of A.
∴{x
: x+5 = 8 }/ ={x : x ∈ N and x≠3}
(ix) Let A
= {x : 2x + 5 = 9 } = {2}
Given
that,
The
set of natural number is the universal set
To
find the complement of the
{x
: 2x+5=9}
The
complement of set A is the set of all elements of U which are not the elements
of A.
2x+5=9
2x=4
x=2
∴{x:2x+5=9}/
={x:x∈N and x≠2 }
(x) Given
that,
The
set of natural number is the universal set
To
find the complement of
{x
: x ≥ 7 }
The
complement of set A is the set of all elements of U which are not the elements
of A.
∴{x
: x≥ 7}/ ={ x : x ∈ N and x 7}
(xi)
Given that,
The
set of natural number is the universal set
To
find the complement of the
{x
: x ∈ N and 2x + 110 }
The
complement of set A is the set of all elements of U which are not the elements
of A.
2x
+ 1 > 10
2x
> 9
X
> 92
∴{
x : x ∈ N and 2x + 110}/
={x : x ∈ N and x ≤92 }
Exercise 1.5 Class 11 Maths Question 4
4. If
U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = {
2, 4, 6, 8 } and B = { 2, 3, 5, 7 } . Verify that
(i)
( A ∪
B )/ = A/ ∩ B/
(ii)
( A ∩
B )/ = A/ ∪ B )/
Solutions:-
Given:
U = {1, 2, 3, 4, 5, 6, 7, 8, 9 },
A
= {2, 4, 6, 8} and B = {2, 3, 5, 7}
(i)
L.H.S. = (A ∪ B)/ = U – (A ∪
B)
=
{1, 2, 3, 4, 5, 6, 7, 8, 9} – ({2, 4, 6, 8} ∪ {2, 3, 5, 7})
=
{1, 2, 3, 4, 5, 6, 7, 8, 9} – {2, 3, 4, 5, 6, 7, 8} = {1, 9}
R.H.S.
= A/ ∩ B/ = (U – A) ∩ (U – B)
=
({1, 2, 3, 4, 5, 6, 7, 8, 9} – {2, 4, 6, 8}) ∩ ({1, 2, 3, 4, 5, 6, 7, 8, 9} –
{2, 3, 5, 7})
=
{1, 3, 5, 7, 9} ∩ {1, 4, 6, 8, 9} = {1, 9}
L.H.S.
= R. H. S.
(A∪B)/=A/∩
B/
(ii)
L.H.S. = (A ∩ B)/
=
U – (A ∪ B)
=
{1, 2, 3, 4, 5, 6, 7, 8, 9} – ({2, 4, 6, 8} ∩ {2, 3, 5, 7})
=
{1, 2, 3, 4, 5, 6, 7, 8, 9} – {2}
=
{1, 3, 4, 5, 6, 7, 8, 9}
R.H.S.
= A/ ∪ B/ = (U – A) ∪
(U – B)
=
({1, 2, 3, 4, 5, 6, 7, 8, 9} – {2, 4, 6, 8}) ∪ ({1, 2, 3, 4, 5, 6, 7, 8, 9} –
{2, 3, 5, 7})
=
{1, 3, 5, 7, 9} ∪ {1, 4, 6, 8, 9}
=
{1, 3, 4, 5, 6, 7, 8, 9}
L.H.S.
= R. H. S.
Hence
it has been proved that (A∩B)/=A/ ∪ B/
Exercise 1.5 Class 11 Maths Question 5
5. Draw appropriate Venn diagram for each of
the following :
(i)
( A ∪
B )/
(ii)
A/
∩ B/
(iii)
( A ∩
B )/
(iv)
A/
∪ B/
Solutions:-
(i)
( A ∪
B )/
(iii) ( A ∩
B )/
(iv) A/
∪ B/
Exercise 1.5 Class 11 Maths Question 6
6. Let U be 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/ ?
Solution:- A/ is the set of all
equilateral triangles .
Exercise 1.5 Class 11 Maths Question 7
7. Fill in the blanks to make each of the
following a true statement :
(i)
A ∪ A/ = . . . .
(ii)
Φ/
∩ A = . . . .
(iii)
A
∩ A/ = . . . .
(iv)
U/
∩ A = . . . . .
Solution:-
(i)
A ∪ A/ = ∪
(ii)
Φ/
∩ A = ∪ ∩ A = A
∴ Φ/ ∩ A = A
(iii)
A
∩ A/ = Φ
(iv)
U/
∩ A = Φ ∩ A = Φ
∴ U/ ∩ A = Φ
Published By Lokesh Das
Class 11 Maths questions Answer.
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