CBSE NCERT Solutions For Class 11th Maths Chapter 1 : Set. NCERT Solutins For Class 11 Mathematics. Exercise 1.1, Exercise 1.2, Exercise 1.3, Exercise 1.4, Exercise 1.5, Exercise 1.6, (Miscellaneous Excercise) many more solutions

**Exercise 1.2**

**Question 1:**

Which of the following are examples of the null set

- Set of odd natural numbers divisible by 2
- Set of even prime numbers
- {
*x*:*x*is a natural numbers,*x*< 5 and*x*> 7 } - {
*y*:*y*is a point common to any two parallel lines} Answer- A set of odd natural numbers divisible by 2 is a null set because no odd number is divisible by 2.
- A set of even prime numbers is not a null set because 2 is an even prime number.

- {
*x*:*x*is a natural number,*x*< 5 and*x*> 7} is a null set because a number cannot be simultaneously less than 5 and greater than 7. - {
*y*:*y*is a point common to any two parallel lines} is a null set because parallel lines do not intersect. Hence, they have no common point.

**Question 2:**

Which of the following sets are finite or infinite

- The set of months of a year
- {1, 2, 3 …}
- {1, 2, 3 … 99, 100}
- The set of positive integers greater than 100
- The set of prime numbers less than 99 Answer

- The set of months of a year is a finite set because it has 12 elements.
- {1, 2, 3 …} is an infinite set as it has infinite number of natural numbers.
- {1, 2, 3 …99, 100} is a finite set because the numbers from 1 to 100 are finite in number.
- The set of positive integers greater than 100 is an infinite set because positive integers greater than 100 are infinite in number.
- The set of prime numbers less than 99 is a finite set because prime numbers less than 99 are finite in number.

**Question 3:**

State whether each of the following set is finite or infinite:

- The set of lines which are parallel to the
*x*-axis - The set of letters in the English alphabet
- The set of numbers which are multiple of 5
- The set of animals living on the earth
- The set of circles passing through the origin (0, 0) Answer
- The set of lines which are parallel to the
*x*-axis is an infinite set because lines parallel to the*x*-axis are infinite in number. - The set of letters in the English alphabet is a finite set because it has 26 elements.

- The set of lines which are parallel to the
- The set of numbers which are multiple of 5 is an infinite set because multiples of 5 are infinite in number.
- The set of animals living on the earth is a finite set because the number of animals living on the earth is finite (although it is quite a big number).
- The set of circles passing through the origin (0, 0) is an infinite set because infinite number of circles can pass through the origin.

**Question 4:**

In the following, state whether A = B or not:

- A = {
*a*,*b*,*c*,*d*}; B = {*d*,*c*,*b*,*a*} - A = {4, 8, 12, 16}; B = {8, 4, 16, 18}
- A = {2, 4, 6, 8, 10}; B = {
*x*:*x*is positive even integer and*x*≤ 10} - (iv) A = {
*x*:*x*is a multiple of 10}; B = {10, 15, 20, 25, 30 …} - Answer

**(i) **A = {*a*,** ***b*,** ***c*,** ***d*}; B = {*d*,** ***c*,** ***b*,** ***a*}

The order in which the elements of a set are listed is not significant.

∴A = B

**(ii) **A = {4, 8, 12, 16}; B = {8, 4, 16, 18}** **It can be seen that 12 ∈ A but 12 ∉ B.

∴A ≠ B

**(iii) **A = {2, 4, 6, 8, 10}

B = {*x*: *x* is a positive even integer and *x* ≤ 10} = {2, 4, 6, 8, 10}

∴A = B

**(iv) **A = {*x*:** ***x*** **is a multiple of 10}** **B = {10, 15, 20, 25, 30 …}

It can be seen that 15 ∈ B but 15 ∉ A.

∴A ≠ B

**Question 5:**

Are the following pair of sets equal? Give reasons.

- A = {2, 3}; B = {
*x*:*x*is solution of*x*^{2}+ 5*x*+ 6 = 0} - A = {
*x*:*x*is a letter in the word FOLLOW}; B = {*y*:*y*is a letter in the word WOLF} Answer

**(i) **A = {2, 3}; B = {*x*:** ***x*** **is a solution of** ***x*^{2}** **+ 5*x*** **+ 6 = 0}** **The equation *x*^{2} + 5*x* + 6 = 0 can be solved as:

*x*(*x *+ 3) + 2(*x *+ 3) = 0* *(*x* + 2)(*x* + 3) = 0

*x *= –2 or* x *= –3

∴A = {2, 3}; B = {–2, –3}

∴A ≠ B

**(ii) **A = {*x*:** ***x*** **is a letter in the word FOLLOW} = {F, O, L, W}** **B = {*y*: *y* is a letter in the word WOLF} = {W, O, L, F}

The order in which the elements of a set are listed is not significant.

∴A = B

**Question 6:**

From the sets given below, select equal sets:

A = {2, 4, 8, 12}, B = {1, 2, 3, 4}, C = {4, 8, 12, 14}, D = {3, 1, 4, 2} E = {–1, 1}, F = {0, *a*}, G = {1, –1}, H = {0, 1}

Answer

A = {2, 4, 8, 12}; B = {1, 2, 3, 4}; C = {4, 8, 12, 14} D = {3, 1, 4, 2}; E = {–1, 1}; F = {0, *a*}

G = {1, –1}; A = {0, 1} It can be seen that

8 ∈ A, 8 ∉ B, 8 ∉ D, 8 ∉ E, 8 ∉ F, 8 ∉ G, 8 ∉ H

⇒ A ≠ B, A ≠ D, A ≠ E, A ≠ F, A ≠ G, A ≠ H Also, 2 ∈ A, 2 ∉ C

∴ A ≠ C

3 ∈ B, 3 ∉ C, 3 ∉ E, 3 ∉ F, 3 ∉ G, 3 ∉ H

∴ B ≠ C, B ≠ E, B ≠ F, B ≠ G, B ≠ H

12 ∈ C, 12 ∉ D, 12 ∉ E, 12 ∉ F, 12 ∉ G, 12 ∉ H

- C ≠ D, C ≠ E, C ≠ F, C ≠ G, C ≠ H 4 ∈ D, 4 ∉ E, 4 ∉ F, 4 ∉ G, 4 ∉ H
- D ≠ E, D ≠ F, D ≠ G, D ≠ H Similarly, E ≠ F, E ≠ G, E ≠ H F ≠ G, F ≠ H, G ≠ H

The order in which the elements of a set are listed is not significant.

- B = D and E = G

Hence, among the given sets, B = D and E = G.

### NCERT Solutions for Class XI Maths: Chapter 1 – Set

**Exercise 1.1 Solutions****Exercise 1.2 Solutions****Exercise 1.3 Solutions****Exercise 1.4 Solutions****Exercise 1.5 Solutions****Exercise 1.6 Solutions****Miscellaneous Solutions**