Maharashtra Board Class 9 Maths Solutions for Chapter 1 Sets – Practice Set 1.2. This comprehensive guide provides all Practice Set 1.2 solutions with step-by-step answers. Learn how to identify equal sets, empty sets, and classify them as finite or infinite sets with proper justifications as per the Maharashtra State Board syllabus. Perfect for Class 9 students preparing for exams.
📝 Q(1) Decide which of the following are equal sets and which are not? Justify your answer.
A = { x | 3x – 1 = 2 }
B = { x | x is a natural number but x is neither prime nor composite. }
C = { x | x ∈ N, x < 2 }
Justification:
👉 For Set A: 3x – 1 = 2 ➔ 3x = 2 + 1 ➔ 3x = 3 ➔ x = 1. Therefore, A = {1}
👉 For Set B: 1 is the only natural number which is neither prime nor composite. Therefore, B = {1}
👉 For Set C: The only natural number smaller than 2 is 1. Therefore, C = {1}
Since the elements of sets A, B, and C are identical, they are equal sets.
📝 Q(2) Decide whether set A and B are equal sets. Give reason for your answer.
A = Even prime numbers
B = { x | 7x – 1 = 13 }
Reason:
👉 For Set A: 2 is the only even prime number. Therefore, A = {2}
👉 For Set B: 7x – 1 = 13 ➔ 7x = 13 + 1 ➔ 7x = 14 ➔ x = 2. Therefore, B = {2}
Since both sets A and B have the exact same element ‘2’, Set A and Set B are equal sets.
📝 Q(3) Which of the following are empty sets? why?
(i) A = { a | a is a natural number smaller than zero. }
Reason: Natural numbers start from 1 (1, 2, 3, …). There is no natural number smaller than zero. Therefore, A = { } or ϕ.
(ii) B = { x | x² = 0 }
Reason: Solving x² = 0 gives x = 0. Therefore, B = {0}. Since the set contains one element (0), it is not an empty set.
(iii) C = { x | 5x – 2 = 0, x ∈ N }
Reason: Solving 5x – 2 = 0 gives 5x = 2 ➔ x = 2/5. Since 2/5 is a fraction and not a natural number (x ∉ N), Set C has no elements. Therefore, C = { } or ϕ.
📝 Q(4) Write with reasons, which of the following sets are finite or infinite.
(i) A = { x | x < 10, x is a natural number }
Reason: A = {1, 2, 3, 4, 5, 6, 7, 8, 9}. The elements in Set A are limited and countable, so it is a finite set.
(ii) B = { y | y < -1, y is an integer }
Reason: B = {…, -5, -4, -3, -2}. There are unlimited integers smaller than -1 and they cannot be counted, so it is an infinite set.
(iii) C = Set of students of class 9 from your school.
Reason: The total number of students in class 9 of a school is fixed and easily countable, so it is a finite set.
(iv) Set of people from your village.
Reason: The population of a village is limited and can be counted, so it is a finite set.
(v) Set of apparatus in laboratory
Reason: The instruments and apparatus kept in a laboratory are limited in number and countable, so it is a finite set.
(vi) Set of whole numbers
Reason: W = {0, 1, 2, 3, 4, …}. Whole numbers continue endlessly and are uncountable, so it is an infinite set.
(vii) Set of rational number
Reason: There are infinitely many rational numbers, and they cannot be counted, so it is an infinite set.
Congratulations on completing Practice Set 1.2! We hope these step-by-step solutions helped you easily understand the concepts of equal sets, empty sets, and finite/infinite sets. Consistent practice is the best way to score high marks in your Maharashtra Board Class 9 Maths exams. Now that you have successfully solved all the questions of Practice Set 1.2, you can move on to the next exercises using the links provided below. Keep learning!
More Solutions for Chapter 1 (Sets):
- 🔗 [Class 9 Math Chapter 1 Practice Set 1.1 Solutions]
- 🔗 [Class 9 Math Chapter 1 Practice Set 1.2 Solutions]
- 🔗 [Class 9 Math Chapter 1 Practice Set 1.3 Solutions]
- 🔗 [Class 9 Math Chapter 1 Practice Set 1.4 Solutions]
- 🔗 [Class 9 Math Chapter 1 Practice Set 1.5 Solutions]
- 🔗 [Problem Set 1 Solutions]
