**Exercise 1.2 Sets**

**Question and Answers**

**Class 11 – Maths**

Class | Class 11 |

Subject | Mathematics |

Chapter Name | Sets |

Chapter No. | Chapter 1 |

Exercise | Exercise 1.2 |

Category | Class 11 Maths NCERT Solutions |

**Question 1 Which of the following are examples of the null set **

**(i) Set of odd natural numbers divisible by 2**

**(i)** There is no odd number that will be divisible by 2 and so this set is a null set.

**(ii) Set of even prime numbers**

**(ii)** There was an even number 2, which will be the one and only even prime number. So the set contains an element. So it is not a null set.

**(iii) {x : x is a natural numbers, x < 5 and x > 7 }**

**(iii)** There was no number that will be less than 5 and greater than 7 simultaneously. So it is a null set.

**(iv) {y : y is a point common to any two parallel lines}**

**(iv)** The parallel lines do not intersect each other. So it does not have a common point of intersection. So it is a null set.

**Question 2 Which of the following sets are finite or infinite**

** (i) The set of months of a year**

**(i)** A year has twelve months which has defined number of elements. Therefore, the set of months of a year is finite.

** (ii) {1, 2, 3, . . .}**

**(ii)** The set consists of an infinite number of natural numbers. Therefore, the set {1, 2, 3 …..} is infinite since it contains an infinite number of elements.

**(iii) {1, 2, 3, . . .99, 100}**

**(iii) **{1, 2, 3 …99, 100} is a finite set as the numbers from 1 to 100 are finite.

**(iv) The set of positive integers greater than 100**

**(iv) **The set of positive integers greater than 100 is an infinite set as the positive integers which are greater than 100 are infinite.

**(v) The set of prime numbers less than 99**

**(v) **The set of prime numbers less than 99 is a finite set as the prime numbers which are less than 99 are finite.

**Question 3 State whether each of the following set is finite or infinite:**

** (i) The set of lines which are parallel to the x-axis**

**(i) **The set of lines which are parallel to the *x*-axis is an infinite set as the lines which are parallel to the *x*-axis are infinite.

** (ii) The set of letters in the English alphabet**

**(ii) **The set of letters in the English alphabet is a finite set as it contains 26 elements.

**(iii) The set of numbers which are multiple of 5**

**(iii)** The set of numbers which are multiple of 5 is an infinite set as the multiples of 5 are infinite.

**(iv) The set of animals living on the earth**

**(iv)** The set of animals living on the earth is a finite set as the number of animals living on the earth is finite.

**(v) The set of circles passing through the origin (0,0)**

**(v) **The set of circles passing through the origin (0, 0) is an infinite set as infinite number of circles can pass through the origin.

**Question 4 In the following, state whether A = B or not: **

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

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

Order in which the elements of a set are listed is not significant. Therefore, A = B.

**(ii) A = { 4, 8, 12, 16 } B = { 8, 4, 16, 18}**

(ii) A = {4, 8, 12, 16}; B = {8, 4, 16, 18}

We know that 12 ∈ A but 12 ∉ B. Therefore, A ≠ B

** (iii) A = {2, 4, 6, 8, 10} B = { x : x is positive even integer and x ≤ 10}**

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

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

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

(iv) A = {*x*: *x* is a multiple of 10}

B = {10, 15, 20, 25, 30 …}

We know that 15 ∈ B but 15 ∉ A. Therefore, A ≠ B

**Question 5 Are the following pair of sets equal? Give reasons.**

** (i) A = {2, 3}, B = {x : x is solution of x 2 + 5x + 6 = 0}**

**(i)** A = {2, 3}; B = { *x*: *x *is solution of *x*^{2} + 5*x *+ 6 = 0}

*x*^{2} + 5*x* + 6 = 0 can be written as *x*(*x* + 3) + 2(*x* + 3) = 0

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

So we get

*x* = –2 or *x* = –3

Here

A = {2, 3}; B = {–2, –3}

Therefore, A ≠ B

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

**(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}

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

Therefore, 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}; H = {0, 1}

We know 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

It can be written as

2 ∈ A, 2 ∉ C

Therefore, A ≠ C

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

B ≠ C, B ≠ E, B ≠ F, B ≠ G, B ≠ H

It can be written as

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

Therefore, C ≠ D, C ≠ E, C ≠ F, C ≠ G, C ≠ H

4 ∈ D, 4 ∉ E, 4 ∉ F, 4 ∉ G, 4 ∉ H

Therefore, D ≠ E, D ≠ F, D ≠ G, D ≠ H

Here, E ≠ F, E ≠ G, E ≠ H

F ≠ G, F ≠ H, G ≠ H

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

B = D and E = G

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

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