In the last chapter, we studied different ways to use sets to make new sets from old ones. In this chapter, you will learn one more operation called the Cartesian product of sets. This operation helps students easily understand the meaning of relations between sets.
If any student finds it hard to understand these topics, they can use the RD Sharma Solutions Class 11 Maths for help.
These solutions are prepared by experienced subject teachers following the latest CBSE syllabus. You can download RD Sharma Class 11 Maths Chapter 2 Solutions in PDF format using the links given below. It is a good idea for students to use these solutions regularly to understand the concepts better and improve their learning.
RD Sharma Solutions for Class 11 Maths Chapter 2 – Relations PDF
Download free PDF of RD Sharma Solutions for Class 11 Maths Chapter 2 – Relations, prepared by expert Maths teachers at home-tuition. You will get step-by-step solutions to all the exercises from Chapter 2. These solutions will help you quickly revise the whole syllabus and score better marks in exams. You can also join online coaching for IIT JEE (Main & Advanced), NEET, and other engineering and medical entrance exams.
Access answers to RD Sharma Solutions for Class 11 Maths Chapter 2 – Relations
1. What is a relation in mathematics?
Answer: A relation shows how elements from one set are connected to elements from another set.
2. What is the Cartesian product of two sets A = {1, 2}, B = {a, b}?
Answer: A × B = {(1, a), (1, b), (2, a), (2, b)}
3. How many ordered pairs are there in A × B if A has 3 elements and B has 2 elements?
Answer: 3 × 2 = 6 ordered pairs.
4. Give an example of a relation from set A = {1, 2} to set B = {3, 4}.
Answer: Relation R = {(1, 3), (2, 4)}
5. What is the total number of relations possible from A = {1, 2} to B = {3, 4}?
Answer: Total relations = 2^(2×2) = 16
6. What is a universal relation?
Answer: A relation where every element of one set is related to every element of another set.
7. What is a void (empty) relation?
Answer: A relation where no elements are related to any other elements.
8. Give an example of a void relation.
Answer: For A = {1, 2}, R = {} is a void relation.
9. If A has 4 elements and B has 3 elements, how many elements are in A × B?
Answer: 4 × 3 = 12 elements.
10. Define reflexive relation.
Answer: A relation where each element is related to itself.
11. Give an example of a reflexive relation.
Answer: For A = {1, 2}, R = {(1, 1), (2, 2)} is reflexive.
12. What is a symmetric relation?
Answer: A relation where (a, b) ∈ R implies (b, a) ∈ R.
13. Give an example of a symmetric relation.
Answer: R = {(1, 2), (2, 1)} is symmetric.
14. Define transitive relation.
Answer: A relation is transitive if (a, b) and (b, c) ∈ R implies (a, c) ∈ R.
15. Give an example of a transitive relation.
Answer: R = {(1, 2), (2, 3), (1, 3)} is transitive.
16. What is an equivalence relation?
Answer: A relation which is reflexive, symmetric, and transitive.
17. Is R = {(a, a)} on A reflexive?
Answer: Yes, every element relates to itself.
18. Is R = {(1, 2), (2, 1)} symmetric?
Answer: Yes, since (1, 2) implies (2, 1).
19. Find A × A if A = {x, y}.
Answer: A × A = {(x, x), (x, y), (y, x), (y, y)}
20. How many relations can be formed on a set A with n elements?
Answer: 2^(n²) relations.
21. If A = {1, 2}, list all possible relations.
Answer: A × A = {(1,1), (1,2), (2,1), (2,2)} → Total 16 possible relations.
22. Define identity relation.
Answer: A relation R = {(a, a): a ∈ A} is called identity relation.
23. Is identity relation reflexive?
Answer: Yes, it is always reflexive.
24. Is identity relation symmetric and transitive?
Answer: Yes, identity relation is reflexive, symmetric, and transitive, making it an equivalence relation.
25. If A = {1, 2, 3}, how many elements are in A × A?
Answer: 3 × 3 = 9 ordered pairs.
Frequently Asked Questions
Chapter 2 explains Relations using sets, ordered pairs, Cartesian products, and introduces the concepts of types of relations like reflexive, symmetric, transitive, and equivalence relations with solved examples.
RD Sharma provides step-by-step solved examples, covers every concept in detail, and includes practice questions that help you build a strong foundation for exams like CBSE, IIT-JEE, and other entrance tests.
Yes, all exercise questions are solved with detailed explanations. You also get miscellaneous exercises and extra questions for revision.
Yes, RD Sharma follows the latest CBSE syllabus, and solving these questions helps you score high marks by understanding the important exam patterns and concepts.
Important topics include:
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Cartesian product of sets
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Types of relations
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Reflexive, symmetric, and transitive relations
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Equivalence relations
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Number of possible relations
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Examples and problem-solving techniques