NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.2 is part of NCERT Solutions for Class 11 Maths. Here we have given NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.2.

- Sets Class 11 Ex 1.1
- Sets Class 11 Ex 1.3
- Sets Class 11 Ex 1.4
- Sets Class 11 Ex 1.5
- Sets Class 11 Ex 1.6
- Sets Class 11 Miscellaneous Exercise

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 11 |

Subject |
Maths |

Chapter |
Chapter 1 |

Chapter Name |
Sets |

Exercise |
Ex 1.2 |

Number of Questions Solved |
6 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.2

**Ex 1.2 Class 11 Maths Question 1.**

**Which of the following are examples of the null set?**

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

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

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

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

**Solution.**

**(i)** Set of odd natural numbers divisible by 2 is a null set because odd natural numbers are not divisible by 2.

**(ii)** Set of even prime numbers is {2} which is not a null set.

**(iii)** {x: x is a natural number, x < 5 and x >7} is a null set because there is no natural number which satisfies x < 5 and x > 7 simultaneously,

**(iv)** [y: y is a point common to any two parallel lines) is a null set because two parallel lines

do not have any common point.

**Ex 1.2 Class 11 Maths Question 2.**

**Which of the following sets are finite or infinite?**

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

**(ii)** {1,2,3,…}

**(iii)** {1,2,3, …,99,100}

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

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

**Solution.**

**(i)** The set of months of a year is finite set because there are 12 months in a year.

**(ii)** {1, 2, 3, …} is an infinite set because there are infinite elements in the set.

**(iii)** {1, 2, 3, …, 99, 100) is a finite set because the set contains finite number of elements.

**(iv)** The set of positive integers greater than 100 is an infinite set because there are infinite

number of positive integers greater than 100.

**(v)** The set of prime numbers less than 99 is a finite set because the set contains finite number of elements.

**Ex 1.2 Class 11 Maths 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

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

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

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

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

**Solution.**

**(i)** The set of lines which are parallel to the x-axis is an infinite set because we can draw infinite number of lines parallel to x-axis.

**(ii)** The set of letters in the English alphabet is a finite set because there are 26 letters in the English alphabet.

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

**(iv)** The set of animals living on the earth is a finite set because the number of animals living on the earth is very large but finite.

**(v)** The set of circles passing through the origin (0, 0) is an infinite set because we can draw infinite number of circles passing through origin of different radii.

**Ex 1.2 Class 11 Maths Question 4.**

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

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

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

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

B = {x : x is positive even integer and x≤ 10}

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

B = {10, 15, 20, 25, 30,…}

**Solution.**

**(i)** A = {a, b, c, d} and B = {d, c, b, a} are equal sets because order of elements does not changes a set.

∴ A = B = [a, b, c, d}.

**(ii)** A = {4, 8, 12, 16} and B = {8, 4, 16, 18} are not equal sets because 12 ∈ A but 12 ∉ B and 18 ∉ B but 18 ∉ A.

**(iii)** A = {2, 4, 6, 8,10} and B = {x: x is a positive even integer and x ≤ 10) which can be written in roster form as B = (2, 4, 6, 8, 10) are equal sets.

∴ A = B = {2, 4, 6, 8,10).

**(iv)** A = {x: x is a multiple of 10) can be written in roster form as A = {10, 20, 30, 40,…….. } and

B – {10, 15, 20, 25, 30, ………..} are not equal sets because 15 ∈ B but 15 ∉ A.

**Ex 1.2 Class 11 Maths 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}

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

B = {y: y is a letter in the word WOLF}

**Solution.**

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

Now, x^{2} + 5x + 6 = 0 ⇒ x^{2} + 3x + 2x + 6 = 0 ⇒ (x + 3)(x + 2) = 0 ⇒ x = -3, -2

∴ B = {-2, -3}

Hence, A and B are not equal sets.

**(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}

Hence, A = B = {F, O, L, W}.

**Ex 1.2 Class 11 Maths 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}

**Solution.**

From the given sets, we see that sets B and D have same elements and also sets E and G have same elements.

∴ B = D = {1 ,2, 3, 4} and E = G = {-1, 1}.

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