1. Express the set of all vowels in the English alphabet in roster form and set-builder form.
Solution:
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RD Sharma Solutions for Class 11 Maths Chapter 1 Sets
The RD Sharma Solutions for Class 11 Chapter 1 Sets PDF is an essential resource for mastering the foundational topic of sets in mathematics. This chapter introduces students to key concepts such as the definition and description of sets, roster and set-builder forms, types of sets, subsets, universal and power sets, Venn diagrams, and various operations on sets like union, intersection, and complement. These concepts are crucial for building a strong base in higher mathematics and are frequently tested in both board and competitive exams.
RD Sharma Solutions for Class 11 Maths Chapter 1 Sets PDF includes:
- Comprehensive, step-by-step solutions for all eight exercises in Chapter 1, ensuring students can follow the logic and methodology behind each answer.
- Detailed examples that clarify complex problems and make it easier for students to understand and apply set theory concepts in different scenarios.
- Extra questions and important problems, including MCQs and advanced-level questions, to reinforce understanding and improve problem-solving skills.
- By regularly practicing with the RD Sharma Solutions for Class 11 Chapter 1 Sets PDF, students can:
- Strengthen their grasp of set theory and related operations, which are foundational for later topics in mathematics.
- Resolve doubts instantly with clear, expert-verified explanations, boosting confidence for board exams and entrance tests.
- Improve speed and accuracy in solving set-related problems, which is vital for achieving high scores.
The solutions are designed to be student-friendly and align with the latest CBSE syllabus, making them suitable for all learners, whether preparing for school exams or competitive entrance tests.
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Download RD Sharma Solutions for Class 11 Maths Chapter 1 Integers PDF Here
Download the RD Sharma Solutions for Class 11 PDF now to access detailed solutions, worked examples, and extra practice questions-all tailored to help you master the concept of sets and excel in mathematics.
With the help of RD Sharma’s solutions, students can easily understand and practice integers, ensuring they have a solid foundation for tackling more complex mathematical topics in the future.
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RD Sharma Solutions For Class 11: Practice Problems
- Roster Form: A = {a, e, i, o, u}
- Set-builder Form: A = {x : x is a vowel in the English alphabet}
2. Find the number of subsets of the set A = {1, 2, 3, 4, 5}.
Solution: Number of subsets = 25 = 32.
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3. If A = {x : x is an even natural number less than 10} and B = {2, 4, 6, 8}, verify that A = B.
Solution: A = {2, 4, 6, 8}, B = {2, 4, 6, 8}. Hence, A = B.
4. If U = {1, 2, 3, ..., 15}, A = {2, 4, 6, 8, 10, 12, 14}, and B = {3, 6, 9, 12, 15}, find:
- (i) A ∪ B = {2, 3, 4, 6, 8, 9, 10, 12, 14, 15}
- (ii) A ∩ B = {6, 12}
- (iii) A' = {1, 3, 5, 7, 9, 11, 13, 15}
5. In a survey of 120 students, 65 students liked Mathematics, 50 liked Physics, and 30 liked both. Find how many students liked neither Mathematics nor Physics.
Solution: Students who liked neither = 120 - (65 + 50 - 30) = 35 students.
6. Let A = {1, 2, 3} and B = {4, 5}. Find the Cartesian product A × B.
Solution: A × B = {(1, 4), (1, 5), (2, 4), (2, 5), (3, 4), (3, 5)}
7. Prove that every set is a subset of itself and the null set is a subset of every set.
Solution: Every set A satisfies A ⊆ A, and the null set Ø is a subset of every set by definition.
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8. If A = {2, 4, 6} and B = {4, 6, 8}, find A ∪ B, A ∩ B, A – B, and B – A.
- A ∪ B = {2, 4, 6, 8}
- A ∩ B = {4, 6}
- A – B = {2}
- B – A = {8}
9. Draw Venn diagrams to illustrate the following relationships:
- (i) A ⊆ B: Circle A is completely inside Circle B.
- (ii) A ∩ B = ∅: Circles A and B do not overlap.
10. Find the number of elements in the power set of a set containing 5 elements.
Solution: Number of elements = 25 = 32.
FAQs: RD Sharma Solutions for Class 11 Maths Chapter 1 Sets
What topics are covered in RD Sharma Solutions for Class 11 Chapter 1 Sets?
The chapter covers essential concepts such as the definition and representation of sets, types of sets (finite, infinite, empty, equal), subsets, power set, universal set, Venn diagrams, operations on sets (union, intersection, difference, complement), and important results related to the number of elements in sets.
What are the different types of sets?
The primary types of sets include:
- Empty (Null) Set
- Singleton Set
- Finite Set
- Infinite Set
- Equal Sets
- Equivalent Sets
- Subset
- Superset
- Universal Set
- Disjoint Sets .
How are sets represented?
Sets are commonly represented in three forms:
- Roster Form (list of elements)
- Set Builder Form (description based on property)
- Statement/Semantic Form (verbal description) .
What is an empty or null set?
An empty set is a set with no elements, symbolized by {} or ∅ .
What is the difference between equal and equivalent sets?
- Equal Sets: Contain precisely the same elements.
- Equivalent Sets: Have the same number of elements but not necessarily identical elements .
What are the main set operations?
- Union (A ∪ B): Elements in A or B or both
- Intersection (A ∩ B): Elements common to both A and B
- Difference (A – B): Elements in A but not in B
- Complement: Elements not in the set but in the universal set .
How many exercises are there in RD Sharma Class 11 Chapter 1 Sets?
There are eight exercises in Chapter 1, each designed to help students practice and master different aspects of set theory with a variety of solved examples and questions.
Why should I use RD Sharma Solutions for Chapter 1 Sets?
RD Sharma Solutions provide step-by-step explanations for each question, making it easier to understand complex concepts. They help clear doubts, strengthen your fundamentals, and are especially useful for board exam and competitive exam preparation.
Are the RD Sharma Solutions for Chapter 1 Sets based on the latest CBSE syllabus?
Yes, the solutions are prepared according to the latest CBSE syllabus and guidelines, ensuring students are well-prepared for their exams.