NCERT Solutions for Class 11 Maths Chapter 1 Sets (Ex 1.4)
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Mathematics is one of the most significant and challenging subjects for students in Class 11. Mathematics requires a strong conceptual understanding as well as a lot of practice in problemsolving. The secret to performing well in mathematics exams is to practice a lot of questions. Chapter 11 of the NCERT Mathematics textbook deals with relations and functions. This chapter should be carefully studied by students because it will likely be covered in the exam.
Formulae, theorems, notions, principles, and other academic content are all included in the broad range of academic content that makes up mathematics. These aspects are inherently linked to one another in a wide variety of fascinating ways. This does not negate the fact that these fundamental concepts and subjects are unique. Due to the academic structure of the scientific field of Mathematics, students must be able to solve individual problems while also understanding the concepts holistically. Calculations that take a long time, formulae made up of a range of numerical and other symbols, and their derivatives working together are all hallmarks of Mathematics as an applied discipline.
The National Council of Educational Research and Training NCERT has been assigned the responsibility to design the textbooks for all classes and subjects in CBSE. CBSE and other state boards and institutions accept NCERT textbooks as the standard reading material for all their examinations. The NCERT textbooks are created in a way that provides the comprehensive education required for the overall development and growth of students’ minds.
NCERT has established a detailed and scientifically organised academic curriculum for Class 11 students studying mathematics. This subject consists of sixteen distinct chapters. Six main units have been used to group these chapters. The result of interdisciplinary research is this classification and the academic information contained in these chapters. The chapters’ arrangement into a logically plausible sequence makes the learning process more fluid and continuous.
The strategically created NCERT books aim to provide an optimum level of education and develop students’ critical and analytical thinking. The NCERT books are standardlevel books, and it is important to have proper guidance and resource material to navigate through them. The NCERT Solutions provide reliable material for students in both English and Hindi mediums for constant guidance and support. Filtering through this data takes up a lot of energy and time, which can leave students less motivated for their actual studies. Hence, using wellfounded and thoroughly researched study material that is available at the tip of the students’ fingers is great support. Students can sccess the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.4 with the problem and solutions of every sum of the exercise.
Students and teachers can use the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.4 for a better understanding of the format and structure that is followed by NCERT Solutions provided by Extramarks. Class 11 is a very crucial level for the students as they also have the Class 12 board examinations approaching. Using the NCERT Solutions Class 11 provided by Extramarks can provide students with the appropriate guidance required for the development of their foundational concepts and topic.
Extramarks also provides the students with past year’s papers and revision notes for all classes These solutions, sample papers, and revision notes can boost the students’ exam preparation. Students should always try to solve as many sample papers as possible before writing the actual examination to boost their confidence.
NCERT Textbooks provide the basis for all national and statelevel competitive examinations. Teachers emphasise the use of these textbooks for all competitive examinations. These books provide foundational knowledge of the subject they are dealing with. Having a companion that helps to go through these crucial texts is very important. NCERT Solutions for each class are designed to cater to the needs of a particular grade students.
Students can download the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.4, and other resources from the Extramarks’ website. The resources are properly categorised according to each class and the resources of the subjects offered.
Students can go through the Extramarks’ website to get access to the NCERT Solutions Class 12, NCERT Solutions Class 11, NCERT Solutions Class 10, NCERT Solutions Class 8, NCERT Solutions Class 7, NCERT Solutions Class 6, NCERT Solutions Class 5, NCERT Solutions Class 4, NCERT Solutions Class 3, NCERT Solutions Class 2 andNCERT Solutions Class 1.
NCERT Solutions for Class 11 Maths Chapter 1 Sets (Ex 1.4) Exercise 1.4
NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.4 is available for download on the Extramarks website in PDF format. Solutions for the Mathematics textbook questions, along with other subjects on the CBSE board, are categorically available on the Extramarks’ website. These NCERT Solutions properly adhere to the NCERT standards and guidelines important for students’ learning and examination. NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.4 has solutions to all the questions in this particular exercise. These exercises are helpful in the preparation of the chapter and revision before the examinations. It might be difficult for some students to tackle all the questions by themselves. Hence, using the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.4, can boost efficiency and morale.
Access NCERT Solutions for Mathematics Chapter 1 – Sets
Class 11 students can access the NCERT solutions for Chapter 1 sets from the Extramarks’ website These solutions will allow the students to have an elaborative understanding of all the important topics and concepts. Going through these solutions will help the students solve the Mathematics questions in a systematic manner. These solutions have been prepared by experts with years of experience. At times students face difficulties in solving Mathematics questions, going through the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.4 will help the students overcome these challenges. The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.4, are compiled by experts with years of experience. These solutions are written in an easytounderstand language.
NCERT Solutions for Class 11 Maths Chapter 1 Sets Exercise 1.4
Class 11 Maths Chapter 1 Exercise 1.4 is the fourth exercise in the chapter of Sets. Using Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.4 for solving the exercise questions will make the process simpler and quicker for the students of Class 11. The chapter on Sets deals with a fixed collection of objects. This chapter has no variations and has fixed elements. These sets are used to form questions that the students have to solve. The topic of Sets includes Subsets and supersets, universal sets, finite and infinite sets, and many other essential topics. The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.4, deals with all the major topics categorically to provide a comprehensive idea of the overall chapter. NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.4, are a very useful tool for scoring higher marks and achieving full conceptual understanding.
The faculty at Extramarks has intricately designed these NCERT solutions to help students through their journey of preparation and examination. The NCERT Solutions like the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.4, are created with utmost care and understanding of the study methods of children. The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.4, has solutions to the topics mentioned in the chapter of Sets with stepbystep guidelines. These guidelines make it easy for the students to understand the subject matter without pressure.
Students should use the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.4 as soon as possible to aid their preparation. It will be advantageous to include the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.4 in their curriculum.
Exercise 1.4
Mathematics needs a lot of practice and constant performance analysis. All the chapters of this subject hold specific scoring values. Using the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.4 helps students understand the methods and techniques required to solve the examination question papers.
The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.4 are compiled by the subject experts at Extramarks. The primary objective of providing the NCERT Solutions is to simplify Mathematics problems in the NCERT textbooks. The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.4, are logically organised and address all the difficulties faced by students solving these exercise questions. The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.4, offer extensive guidance and help students advance their logical and reasoning skills as well as their arithmetic expertise. The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.4, make the learning process comfortable by simplifying and clarifying complicated topics.
Q.1 Find the union of each of the following pairs of sets:
(i) X = {1, 3, 5} Y = {1, 2, 3}
(ii) A = [ a, e, i, o, u} B = {a, b, c}
(iii) A = {x: x is a natural number and multiple of 3}
B = {x: x is a natural number less than 6}
(iv) A = {x: x is a natural number and 1 < x ≤ 6}
B = {x: x is a natural number and 6 < x < 10}
(v) A = {1, 2, 3}, B = Φ
Ans.
(i) X = {1, 3, 5} Y = {1, 2, 3}
X ∪ Y = {1, 2, 3, 5}
(ii) A = [a, e, i, o, u} B = {a, b, c}
A ∪ B = {a, b, c, e, i, o, u}
(iii )A = {x: x is a natural number and multiple of 3}
= {3, 6, 9, 12, 15, … }
B = {x: x is a natural number less than 6}
= {1, 2, 3, 4, 5}
A∪B = {1, 2, 3, 4, 5, 6, 9, 12, 15, …}
(iv) A = {x: x is a natural number and 1 < x ≤ 6}
= {2, 3, 4, 5, 6}
B = {x: x is a natural number and 6 < x < 10}
= {5, 6, 7, 8, 9}
A ∪ B = {2, 3, 4, 5, 6, 7, 8, 9}
(v) A = {1, 2, 3}, B = Φ
A ∪ B = {1, 2, 3} = A
Q.2 Let A = {a, b}, B = {a, b, c}. Is A ⊂ B?
What is A ∪ B?
Ans.
Since, all the elements of set A belongs to the set B,
So, A ⊂ B.
A ∪ B = {a, b, c} = B
Q.3 If A and B are two sets such that A ⊂ B, then what is A ∪ B?
Ans. Since, A ⊂ B so, all the elements of set A belong to set B, then A ∪ B = B.
Q.4 If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find
(i) A ∪ B
(ii) A ∪ C
(iii) B ∪ C
(iv) B ∪ D
(v) A ∪ B ∪ C
(vi) A ∪ B ∪ D
(vii) B ∪ C ∪ D
Ans.
(i) A ∪ B = {1, 2, 3, 4, 5, 6}
(ii) A ∪ C = {1, 2, 3, 4, 5, 6, 7, 8}
(iii) B ∪ C = {3, 4, 5, 6, 7, 8}
(iv) B ∪ D = {3, 4, 5, 6, 7, 8, 9, 10}
(v) A ∪ B ∪ C = {1, 2, 3, 4, 5, 6, 7, 8}
(vi) A ∪ B ∪ D = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
(vii) B ∪ C ∪ D = {3, 4, 5, 6, 7, 8, 9, 10}
Q.5 If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find
(i) A ∩ B
(ii) B ∩ C
(iii) A ∩ C ∩ D
(iv) A ∩ C
(v) B ∩ D
(vi) A ∩ (B ∪ C)
(vii) A ∩ D
(viii) A ∩ (B ∪ D)
(ix) (A ∩ B) ∩ (B ∪ C)
(x) (A ∪ D) ∩ (B ∪ C)
Ans.
(i) A ∩ B = {7, 9, 11}
(ii) B ∩ C = {11, 13}
(iii) A ∩C ∩ D = {} = Φ
(iv) A ∩ C = {11}
(v) B ∩ D = {} = Φ
(vi) A ∩ (B ∪C) = {3, 5, 7, 9, 11} ∩ {7, 9, 11, 13, 15}
= {7, 9, 11}
(vii) A ∩ D = {} = Φ
(viii) A ∩ (B ∪ D)
= {3, 5, 7, 9, 11} ∩ {7, 9, 11, 13, 15, 17}
= {7, 9, 11}
(ix) (A ∩ B ) ∩ ( B ∪ C )
= {7, 9, 11} ∩ {7, 9, 11, 13, 15}
= {7, 9, 11}
(x) (A ∪ D) ∩ (B ∪ C)
= {3, 5, 7, 9, 11, 15, 17} ∩ {7, 9, 11, 13, 15}
= {7, 9, 11, 15}
Q.6 If A = {x: x is a natural number },
B = {x: x is an even natural number}
C = {x: x is an odd natural number} and
D = {x: x is a prime number}, find
(i) A ∩ B
(ii) A ∩ C
(iii) A ∩ D
(iv) B ∩ C
(v) B ∩ D
(vi) C ∩ D
Ans.
A = {x: x is a natural number}
= {1, 2, 3, 4, 5, 6, 7, …}
B = {x: x is an even natural number}
= {2, 4, 6, 8, …}
C = {x: x is an odd natural number}
= {1, 3, 5, 7, …}
D = {x: x is a prime number}
= {2, 3, 5, 7,…}
(i) A∩B = {2, 4, 6, …} = B
(ii) A∩C = {1, 3, 5, 7, …} = C
(iii) A ∩ D = {2, 3, 5, 7,…} = D
(iv) B ∩ C = {} = Φ
(v) B ∩ D = {2}
(vi) C ∩ D = {3, 5, 7, …}
= {x: x is an odd prime number}
Q.7 Which of the following pairs of sets are disjoint
(i) 1, 2, 3, 4} and {x: x is a natural number and 4 ≤ x ≤ 6 }
(ii) {a, e, i, o, u} and { c, d, e, f}
(iii) {x: x is an even integer} and {x: x is an odd integer}
Ans.
(i) Let A = {1, 2, 3, 4} and
B = {x: x is a natural number and 4 ≤ x ≤ 6 } = {4, 5, 6}
A ∩ B = {4}
So, sets A and B are not disjoint sets.
(ii) Let P = {a, e, i, o, u} and Q = {c, d, e, f}
P ∩ Q = {e}
So, sets P and Q are disjoint sets.
(iii) Let C = {x: x is an even integer}
= {…, – 4, – 2, 2, 4, 6, … }
D = {x: x is an odd integer}
= {…, –5, –3, –1, 1, 3, 5,…}
C ∩ D = {} = Φ
So, sets C and D are disjoint sets.
Q.8 If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}; find
(i) A – B
(ii) A – C
(iii) A – D
(iv) B – A
(v) C – A
(vi) D – A
(vii) B – C
(viii) B – D
(ix) C – B
(x) D – B
(xi) C – D
(xii) D – C
Ans.
(i) A – B = {3, 6, 9, 15, 18, 21}
(ii) A – C = {3, 9, 15, 18, 21}
(iii) A – D = {3, 6, 9, 12, 18, 21}
(iv) B – A = {4, 8, 16, 20}
(v) C – A = {2, 4, 8, 10, 14, 16}
(vi) D – A = {5, 10, 20}
(vii) B – C = {20}
(viii) B – D = {4, 8, 12, 16}
(ix) C – B = {2, 6, 10, 14}
(x) D – B = {5, 15, 20}
(xi) C – D = {2, 4, 6, 8, 12, 14, 16}
(xii) D – C = {5, 15, 20}
Q.9 If R is the set of real numbers and Q is the set of rational numbers, then what is R – Q?
Ans.
Since, R = set of real numbers Q = set of rational numbers Therefore,
R – Q = Set of irrational numbers
Q.10 State whether each of the following statement is true or false. Justify your answer.
(i) {2, 3, 4, 5} and {3, 6} are disjoint sets.
(ii) {a, e, i, o, u } and { a, b, c, d }are disjoint sets.
(iii) {2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets.
(iv) {2, 6, 10} and {3, 7, 11} are disjoint sets.
Ans.
(i) False,
Since, {2, 3, 4, 5} ∩ {3, 6} = {3}
So, given sets are not disjoint sets.
(ii) False,
Since, {a, e, i, o, u} ∩{a, b, c, d}= {a}
So, given sets are not disjoint sets.
(iii) True,
Since, {2, 6, 10, 14} ∩ {3, 7, 11, 15} = {}
= Φ
So, given sets are disjoint sets.
(iv) True,
Since, {2, 6, 10} ∩ {3, 7, 11} = {}
= Φ
So, given sets are disjoint sets.
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FAQs (Frequently Asked Questions)
1. Why is it important to solve the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.4?
The NCERT Solutions are crucial for reference while solving the NCERT exercise questions. The stepbystep solutions to the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.4 provide the students with a thorough understanding. These methods can be incorporated by students into their revision notes. Students can overcome this with the use of the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.4.
2. How many questions are there in Class 11 Mathematics Chapter 1 Exercise 1.4?
Class 11 Mathematics Chapter 1 Exercise 1.4 consists of 12 questions in total. These problems are based on the intersection and union of sets. This exercise consists of a number of issues based on the techniques used to represent sets. The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.4 are compiled to help the students gain a deeper understanding of the union and intersection of sets’ attributes. These solutions are thorough and accurate. Every problem is resolved using the appropriate procedure or technique. The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.4 can be used by students for their exam preparation to help them achieve higher marks.