RD Sharma Solutions for Class 11 Maths Chapter 1 – Sets are made by expert teachers of Home-tution. These solutions help students solve problems easily and quickly. The step-by-step answers are written in a clear and simple way so that students can understand them better.
Introduction to Class 11 Maths Chapter 1: Sets – Solutions
The first chapter of Class 11 Maths, "Sets", is an important topic that forms the base of many higher-level mathematical concepts. A set is a collection of well-defined objects. In this chapter, students learn how to represent sets, types of sets, Venn diagrams, and operations like union, intersection, and complement. The RD Sharma Class 11 Solutions for Chapter 1: Sets provides clear explanations and step-by-step answers to all questions. These solutions help students understand each concept better and improve their problem-solving skills.
Exercises Covered in Chapter 1 – Sets:
- Exercise 1.1 – Introduction to Sets
- Exercise 1.2 – Types of Sets
- Exercise 1.3 – Venn Diagrams
- Exercise 1.4 – Operation on Sets
- Exercise 1.5 – Complement of a Set
- Exercise 1.6 – Practical Problems on Union and Intersection
Each exercise in the RD Sharma Solutions includes easy-to-follow steps to help students solve questions accurately and understand the logic behind them.
RD Sharma Solutions Class 11 Maths Chapter 1 - Sets Question with Answers
Q1. Define a set and give two examples.
Answer:
A set is a well-defined collection of distinct objects.
Examples:
-
Set of vowels in the English alphabet: {a, e, i, o, u}
-
Set of even numbers less than 10: {2, 4, 6, 8}
Q2. Write the following sets in roster form:
(i) A = {x: x is a natural number less than 7}
(ii) B = {x: x is a letter in the word ‘MATHS’}
Answer:
(i) A = {1, 2, 3, 4, 5, 6}
(ii) B = {M, A, T, H, S}
Q3. If A = {1, 2, 3}, B = {3, 4, 5}, find:
-
(i) A ∪ B = {1, 2, 3, 4, 5}
-
(ii) A ∩ B = {3}
-
(iii) A − B = {1, 2}
Q4. If U = {1,2,3,4,5,6,7,8}, A = {2,4,6}, find A'.
Answer:
A' (complement of A) = U − A = {1, 3, 5, 7, 8}
Q5. Prove that (A ∪ B)' = A' ∩ B' using Venn Diagram logic.
Answer:
According to De Morgan’s Law: (A ∪ B)' = A' ∩ B'
Explanation: The elements not in A ∪ B are exactly those that are not in A and not in B. So the result holds true.
Q6. If A = {x: x is a prime number less than 10}, list the elements.
Answer: A = {2, 3, 5, 7}
Q7. Show that A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
Answer:
Let x ∈ A ∩ (B ∪ C) → x ∈ A and x ∈ (B ∪ C) → x ∈ A and (x ∈ B or x ∈ C) → x ∈ (A ∩ B) or x ∈ (A ∩ C)
⇒ x ∈ (A ∩ B) ∪ (A ∩ C). Hence proved.
Q8. What is the power set of A = {1, 2}?
Answer:
P(A) = { {}, {1}, {2}, {1, 2} }
Q9. How many elements will the power set of a set with 3 elements have?
Answer:
23 = 8 elements
Q10. Is the following set finite or infinite?
A = {x | x is a natural number divisible by 5}
Answer:
The set is infinite as it includes all multiples of 5.
Why Should All the Students Go Through the RD Sharma Class 11 Sets Solutions?
Students are advised to follow a routine and regularly practice RD Sharma Class 11 Sets Solutions for better exam preparation. These solutions help build a strong base in Maths and make it easier to understand all the topics. Our expert teachers have explained each concept clearly, which helps students feel confident and improve their problem-solving and thinking skills. RD Sharma Class 11 Sets Solutions is one of the best study materials for students. It not only boosts confidence and motivation but also helps in improving memory and speed. These solutions follow the latest syllabus and cover all important topics and methods. The solutions are written in a simple and easy way so that students can understand the topic step by step. By using these solutions, students can learn Sets better and increase their chances of scoring good marks in exams.