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:(i) {a, b} ⊄ {b, c, a}
(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) Ø ∈ A
(x) Ø ⊂ A
(xi) {Ø} ⊂ A
Solution.
Ex 1.3 Class 11 Maths Question 4.
Write down all the subsets of the following sets:(i) {a}
(ii) {a, b}
(iii) {1, 2, 3}
(iv) φ
Solution.
(i) {a}
Number of elements in the given
set = 1
Number of subsets of the given set = 21 = 2
∴ Subsets of the given set are φ, {a}.
(ii) {a, b}
Number of elements in the
given set = 2
Number of subsets of the given set = 22 = 4
∴ Subsets of the given set are φ, {a},
{b}, {a, b}.
(iii) {1, 2, 3}
Number of elements in the
given set = 3
Number of subsets of the given set = 23 = 8
∴ Subsets of the given set are φ, {1}, {2},
{3}, {1, 2}, {2, 3}, {1, 3}, {1, 2, 3}.
(iv) φ
Number of elements in the
given set = 0
Number of subsets of the given set = 20= 1
∴ Subset of the given set is φ.
Ex 1.3 Class 11 Maths Question 5.
Write the following as intervals:(i) {x: x ∈ R, -4 < x ≤ 6}
(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:(i) (-3, 0)
(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) φ
(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) φ
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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