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NCERT Exemplar Class 11 Maths Chapter 1 Solutions: Sets

NCERT Exemplar Solutions for Class 11 Maths Chapter 1 – Sets illustrate the concept of sets and their representation. These solutions are solved by the expert maths teachers at Instasolv as per the latest guidelines of CBSE. The main aim to provide these exemplar solutions is to help you to revise the chapter of NCERT Exemplar Class 11 Maths and clear your concepts for the entrance exams like JEE and NEET.

Some of the main topics of this NCERT Exemplar Solutions for Maths Class 11 Chapter 1 include the empty set, finite and infinite sets, subsets, Venn diagrams, the union of sets, the intersection of sets, the difference of sets, intervals as subsets of R, power set, the complement of a set, subsets, and more.

Chapter 1 has 3 main exercises with around 73 questions in total. The different types of questions available are short answer type questions, long answer type questions, and multiple answer type questions. In this chapter, you will solve a variety of questions based on individual topics and classified sets.

Important Topics for NCERT Maths Exemplar Solutions Class 11 Chapter 1 – Sets

What is a Set?

A set is a group of numbers, considered as a unit into itself. Sets are generally symbolized by italicized, uppercase, boldface letters such as A, B, S, or Z. Each number in a set is referred to as an element of the set. For example, the set of all computers in the world, the set of all irrational numbers between 0 and 1, and the set of all apples on a tree.

The Representation of Set

When the elements of a set can be listed, it is usual to enfold the list in coiled brackets. For example, the set of all-natural numbers between, and including, 11 and 17 as:

K = {11, 12, 13, 14, 15, 16, 17}

Important Equations of Set

  • For any two sets E and F,
  • (E ∪ F)′ = E′ ∩ F′
  • (E ∩ F)′ = E′ ∪ F′
  • If E and F are finite sets such that E ∩ F = ф, then n (E ∪ F) = n (E) + n (F).
  • If E ∩ F ≠ ф, then
    n (E ∪ F) = n (E) + n (F) – n (E ∩ F)
  • n (E ∪ F ∪ G) = n(E) + n(F) + n(G) – n(E ∩ F) – n(E ∩ F) – n(E ∩ F) + n(E ∩ F ∩ G)
  • If E is a subset of set U (Universal Set), then its complement (E′) is also a subset of Universal Set (U).

Some Properties of Operation of Intersection

  • ф ∩ E = ф, U ∩ E = E
  • E ∩ E = E (Idempotent law)
  • E ∩ F = F ∩ E (Commutative law)
  • (E ∩ F) ∩ G = E ∩ (F ∩ G) (Associative law)
  • E ∩ (F ∪ G) = (E ∩ F) ∪ (E ∩ F) (Distributive law)

Some Properties of the Operation of Union

  • U ∪ E = U (Law of U)
  • E ∪ F = F ∪ E (Commutative law)
  • E ∪ ф = E (Law of the identity element)
  • (E ∪ F) ∪ G = E ∪ (F ∪ G) (Associative law)

Exercise-wise Discussion of NCERT Maths Exemplar Solutions Class 11 Chapter 1 – Sets

  • Chapter 1 of NCERT Exemplar Class 11 for Maths has different types of exercises based on the topics discussed above. 
  • The first exercise of the chapter begins with the short answer type questions that are based on a basic introduction to sets and their representations. 
  • In the second exercise, you will find the long answer type questions based on important equations and properties of sets that will strengthen your concepts.
  • In the other exercises, there are multiple-choice questions where your analyzing skills will be put to test. These questions are based on finite sets, union and intersection of sets, subsets and complement of sets.  In these questions, you are required to choose the correct answer out of the four options given.
  • Then, there are state true or false and fill in the blanks questions related to union, subtraction, complement and intersection of sets, universal sets, subsets etc. 

Why Use NCERT Maths Exemplar Solutions Class 11 Chapter 1 – Sets by Instasolv?

  • NCERT Class 11 Maths Exemplar Solutions for Chapter 1 covers all the questions provided in the NCERT Exemplar textbook.
  • These NCERT exemplar solutions are developed by the experts at Instasolv and are an inclusive study material to prepare for class 11 exams.
  • These solutions provided by Instasolv are easily available online.
  • NCERT Exemplar books have been recommended for years as a comprehensive source of material to CBSE students, to improve their analytical skills.
  • They have proven to be essential for learning the syllabus and developing the confidence that is required to face their exams.
  • The NCERT exemplar solutions describe the steps with accuracy, without skipping on important aspects of solving a question.