In the last Maths 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.