Exercise 1.3 NCERT Class 11 Mathematics Chapter 1 Sets contains 8 questions. These questions are basic in nature.
The questions of Exercise 1.3 NCERT Class 11 are formed on the topics such as subsets of sets, real number intervals, and universal sets.
Exercise 1.3 NCERT Class 11 contains questions on topics such as subsets, intervals as subsets of R, and Universal sets.
We have solved Exercise 1.1, Exercise 1.2 and all other exercises from this book.
Exercise 1.3 NCERT Class 11 Math Solutions
1. Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces:
(i) {2, 3, 4} . . . {1, 2, 3, 4, 5}
Answer
{2, 3, 4} ⊂ {1, 2, 3, 4, 5} as all elements of {2, 3, 4} also belongs to the set {1, 2, 3, 4, 5}
(ii)
Answer
⊄ as elements and are not common in both sets.
(iii) {x : x is a student of Class XI of your school} . . . {x : x is a student of your school.}
Answer
⊂ as every student of class XI of your school 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}
Answer
⊄ as a circle in the plane can have different radius than 1 unit.
(v) {x : x is a triangle in a plane} . . . {x : x is a rectangle in the plane}
Answer
⊄ as a triangle is not equal to a rectangle.
(vi) {x : x is an equilateral triangle in a plane} . . . {x : x is a triangle in the same plane}
Answer
⊂ as every equilateral triangle is a triangle.
(vii) {x : x is an even natural number} . . . {x : x is an integer}
Answer
⊂ as all even natural numbers are also an integer.
2. Examine whether the following statements are true or false:
(i) ⊄
Answer
False
Since ⊂ as belongs to both sets
(ii) ⊂
Answer
True
As and are vowels in the English alphabet.
(iii) {1, 2, 3} ⊂ {1, 3, 5}
Answer
False
As 2 ∉
(iv) ⊂
Answer
True
As ∈ and ∈
(v) ∈
Answer
False
As the element ∉
(vi) {x : x is an even natural number less than 6} ⊂ {x : x is a natural number which divides 36}
Answer
The Roster form of the given sets are :
is an even natural number less than 6 =
is a natural number which divides 36 =
Clearly, ⊄
False
3. Let A = {1, 2, {3, 4}, 5}. Which of the following statements are incorrect and why?
(i) {3, 4} ⊂ A
Answer
The statement ⊂ is incorrect. Because it is not a subset of the set A. It is an element of the set A.
So, the correct statement is ∈ or ⊂
(ii) {3, 4} ∈ A
Answer
Correct as explained in (i).
(iii) {{3, 4}} ⊂ A
Answer
Correct Because it is a subset of the set A as explained in (i).
(iv) 1 ∈ A
Answer
Correct
Because 1 is an element of the set A.
(v) 1 ⊂ A
Answer
Incorrect as 1 is an element of set A and not a subset of set A.
(vi) {1, 2, 5} ⊂ A
Answer
Correct as all elements of the set {1, 2, 5} belongs to set A.
(vii) {1, 2, 5} ∈ A
Answer
Incorrect as {1, 2, 5} is not an element of the set A.
(viii) {1, 2, 3} ⊂ A
Answer
Incorrect because 3 ∈ {1, 2, 3} but 3 ∉ A.
(ix) ∈ A
Answer
Incorrect as represents an empty set. Clearly, an empty set does not belong to A. But, it can definitely be a subset of A.
(x) ⊂ A
Answer
Correct as an empty set is subset of every set.
(xi) ⊂ A
Answer
Incorrect as ⊂ A means ∈ A, but it's not true because an empty set is not an element of set A. But it is definitely a subset of A.
4. Write down all the subsets of the following sets
(i)
Answer
The subsets of the set are
(ii)
Answer
The subsets of the set are :
(iii) {1, 2, 3}
Answer
The subsets of the set are:
(iv)
Answer
is the empty set. Empty set is the lowest set possible. The only subset of empty set is itself i.e.
5. Write the following as intervals:
(i) ∈ R,
Answer
The set ∈ R, can be written as interval as follows:
(ii) ∈ R,
Answer
The set ∈ R, can be written as interval as follows:
(iii) ∈ R,
Answer
The set ∈ R, can be written as interval as follows:
(iv) ∈ R,
Answer
The set ∈ R, can be written as interval as follows:
6. Write the following intervals in set-builder form:
(i) (-3, 0)
Answer
The set-builder form of the set (-3, 0) is as follows:
∈ R,
(ii) [6, 12]
Answer
The set-builder form of the set [6, 12] is as follows:
∈ R,
(iii) (6, 12]
Answer
The set-builder form of the set [6, 12] is as follows:
∈ R,
(iv) [-23, 5)
Answer
The set-builder form of the set [-23, 5] is as follows:
∈ R,
7. What universal set(s) would you propose for each of the following:
(i) The set of right triangles.
Answer
The universal set for the set of right triangles would be :
(i) The set of triangles. It is correct because it encompasses all the right triangles.
(ii) The set of isosceles triangles.
Answer
The universal set for the set of isosceles triangles would be :
(i) The set of triangles. It is correct because it encompasses all the right triangles.
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}
Answer
The universal set corresponding to the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8} would be that set which contains at least each element of the given sets. So, from the given examples the correct universal set will be
(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
This exercise 1.3 NCERT Class 11 is one of the easiest exercises in the whole book. It contains one hard question if one may find. This is question no. 4 that asks to find subsets of a given set.
Exercise 1.3 NCERT Class 11 contains conceptual questions. Without the knowledge of basics, one may find it difficult to answer.
Exercise 1.3 NCERT Class 11 contains questions of the following types: (i) Fill in the blanks type (ii) True or False type (iii) Correct or Incorrect type (iv) Finding subsets of a given set type (v) Writing sets as intervals types (vi) Determine the universal sets type.
