**NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.3**

**Ex 1.3 Class 11 Maths Question 1.**

Make correct statements by filling in the symbols ⊂ or ⊄ in the
blank spaces:**(i)**{2, 3, 4} …{1, 2, 3, 4, 5}

**(ii)**{a, b, c}… {b, c, d}

**(iii)**{x: x is a student of Class XI of your school} … {x: x is a student of your school}

**(iv)**{x: x is a circle in the plane}… {x: x is a circle in the same plane with radius 1 unit}

**(v)**{x: x is a triangle in a plane}… {x: x is a rectangle in the plane}

**(vi)**{x: x is an equilateral triangle in a plane} … {x: x is a triangle in the same plane}

**(vii)**{x: x is an even natural number}… {x: x is an integer}

**Solution.**

**(i)** {2, 3, 4} ⊂ {1, 2, 3,
4, 5}

**(ii)** {a, b, c} ⊄ {b, c, d}

**(iii)** {x: x is a student of Class XI of your school} ⊂ {x : x a
student of your school}

**(iv)** {x: x is a circle in the plane} ⊄ {x: x is a
circle in the same plane with radius 1 unit}

**(v)** {x: x is a triangle in a plane} ⊄ {x: x is a
rectangle in the plane}

**(vi)** {x: x is an equilateral triangle in a plane} ⊂ {x: x is a
triangle in the same plane}

**(vii)** {x: x is an even natural number} ⊂ {x: x is
an integer}

**Ex 1.3 Class 11 Maths Question
2.**

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

**(i)****(ii)**{a, e} ⊂ {x: x is a vowel in the English alphabet}

**(iii)**{1, 2, 3} ⊂ {1, 3, 5}

**(iv)**{a} ⊂ {a, b, c}

**(v)**{a} ∈ {a, b, c}

**(vi)**{x: x is an even natural number less than 6} ⊂ {x: x is a natural number which divides 36}

**Solution.**

**Ex 1.3 Class 11 Maths Question 3.**

Let A = {1,
2, {3, 4}, 5}. Which of the following statements are incorrect and why?**(i)**{3, 4} ⊂ A

**(ii)**{3, 4} ∈ A

**(iii)**{{3, 4}} ⊂ A

**(iv)**1 ∈ A

**(v)**1 ⊂ A

**(vi)**{1, 2, 5} ⊂ A

**(vii)**{1, 2, 5} ∈ A

**(viii)**{1, 2, 3} ⊂ A

**(ix)**Ã˜ ∈ A

**(x)**Ã˜ ⊂ A

**(xi)**{Ã˜} ⊂ A

**Solution.**

**Ex 1.3 Class 11
Maths Question 4.**

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

**(i)****(ii)**{a, b}

**(iii)**{1, 2, 3}

**(iv)**Ï†

**Solution.**

**(i)** {a}

Number of elements in the given
set = 1

Number of subsets of the given set = 2^{1} = 2

∴ Subsets of the given set are Ï†, {a}.

**(ii)** {a, b}

Number of elements in the
given set = 2

Number of subsets of the given set = 2^{2} = 4

∴ Subsets of the given set are Ï†, {a},
{b}, {a, b}.

**(iii)** {1, 2, 3}

Number of elements in the
given set = 3

Number of subsets of the given set = 2^{3} = 8

∴ Subsets of the given set are Ï†, {1}, {2},
{3}, {1, 2}, {2, 3}, {1, 3}, {1, 2, 3}.

**(iv)** Ï†

Number of elements in the
given set = 0

Number of subsets of the given set = 2^{0}= 1

∴ Subset of the given set is Ï†.

**Ex 1.3 Class 11 Maths Question
5.**

Write
the following as intervals:**{x: x ∈ R, -4 < x ≤ 6}**

**(i)****(ii)**{x: x ∈ R, -12 < x < -10}

**(iii)**{x: x ∈ R, 0 ≤ x < 7}

**(iv)**{x: x ∈ R, 3 ≤ x ≤ 4}

**Solution.**

**(i)
**Let A = {x: x ∈
R, -4 < x ≤ 6}

It can be written in the form of interval as (-4, 6]

**(ii)** Let
A = {x: x ∈ R, -12 < x < -10}

It can be written in the form of interval as (-12, -10)

**(iii)** Let
A = {x: x ∈ R, 0 ≤ x < 7}

It can be written in the form of interval as [0, 7).

**(iv)** Let
A = {x: x ∈ R, 3 ≤ x ≤ 4}

It can be written in the form of interval as [3, 4].

**Ex 1.3 Class 11
Maths Question 6.**

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

**(i)****(ii)**[6, 12]

**(iii)**(6, 12]

**(iv)**[-23, 5)

**Solution.**

**(i)** The
interval (-3, 0) can be written in set-builder form as {x: x ∈ R, -3 < x < 0}.

**(ii)** The
interval [6, 12] can be written in set-builder form as {x: x ∈ R, 6 ≤ x ≤ 12}.

**(iii)** The
interval (6, 12] can be written in set-builder form as {x: x ∈ R, 6 < x ≤ 12}

**(iv)** The
interval [-23, 5) can be written in set-builder form as {x: x ∈ R, -23 ≤ x < 5}

**Ex 1.3 Class 11
Maths Question 7.**

What universal set(s) would you propose for each of the following:**(i)**The set of right triangles.

**(ii)**The set of isosceles triangles.

**Solution.**

**(i)** Right
triangle is a type of triangle. So, the set of triangles contain all types of
triangles.

∴ U = {x: x is a triangle in a plane}

**(ii)** Isosceles triangle is a type of
triangle. So, the set of triangles contain all types of triangles.

∴ U = {x: x is a triangle in a plane}

**Ex 1.3 Class 11
Maths Question 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 universal set(s) for all the three sets A, B
and C?**(i)**{0, 1, 2, 3, 4, 5, 6}

**(ii)**Ï†

**(iii)**{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

**(iv)**{1, 2, 3, 4, 5, 6, 7, 8}

**Solution.**

**(i)** {0,
1, 2, 3, 4, 5, 6} is not a universal set for A, B, C because 8 ∈ C but 8 is not a member of {0, 1, 2, 3,
4, 5, 6}.

**(ii)** Ï†
is a set which contains no element. So, it is not a universal set for A, B, C.

**(iii)** {0,
1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is a universal set for A, B, C because all
members of A, B, C are present in {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

**(iv)** {1,
2, 3, 4, 5, 6, 7, 8} is not a universal set for A, B, C because 0 ∈ C but 0 is not a member of {1, 2, 3, 4,
5, 6, 7, 8}.

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