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Mathematics · Class 11 Science

Ch 1Sets — Class 11 Mathematics, concept-first.

A set is a well-defined collection of distinct objects. "Well-defined" means that, given any object, we can say with certainty whether it belongs to the collection or not.

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Key concepts

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Complement of a Set

The complement of a set A, denoted A' (or Ac), is defined relative to a fixed universal set U as everything in U that is NOT in A: A' = x / x∈U, x∉A.

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CA Foundation

2 concepts · 4 appearances

2026, 2025, 2023

Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

1.1

Sets and Their Representations

A set is a well-defined collection of distinct objects. "Well-defined" means that, given any object, we can say with certainty whether it belongs to the collection or not.

1.2

Types of Sets — Empty, Finite, Infinite and Equal Sets

Sets can be classified by how many elements they contain, and we can also ask when two sets, described differently, are actually the same set.

1.3

Subsets and Intervals as Subsets of R

Subsets. A set is called a subset of a set , written , if every element of is also an element of . Formally, If but (that is, has at least one element not in ), we say is a proper subset of , written…

1.4

Power Set and Universal Set

Power set. Given a set , the power set of , written , is the set of all possible subsets of — including and itself.

1.5

Venn Diagrams

Sets and the relationships between them can be pictured using simple diagrams introduced by the British logician John Venn, called Venn diagrams.

1.6

Union and Intersection of Sets

Given two sets, the two most fundamental ways of combining them are union and intersection.

1.7

Difference of Sets

Difference of sets. The difference of two sets and (in that order), written (also read " minus "), is the set of elements that belong to but do not belong to :

1.8

Complement of a Set and Its Properties

Complement of a set. Once a universal set has been fixed, the complement of a set (with ), written (or , or ), is the set of all elements of that do not belong to :

Summary

This chapter built the language of sets from the ground up.

Sample & Board Papers

Sample papers and previous-year board questions for this subject.

+Show 1 question1 question
  1. Q1Let A = {x∈N : x²-5x+6=0}, B = {x∈W : 0≤x<2} and C = {x∈N : x<3}, then verify that A×(B∪C) = (A×B)∪(A×C).Preview

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27 Q
+Show 3 questions3 questions
  1. Q25Let $U = \{1, 2, \dots, 20\}$, $A = \{x : x \text{ is even}, x \le 20\}$, $B = \{x : x \text{ is a multiple of } 5, x \le 20\}$. Find $A$, $…Free
  2. Q26If $A$, $B$, $C$ are subsets of a universal set $U$ such that $A \subseteq B$ and $B \subseteq C$, prove that $A \subseteq C$. Verify this u…Preview
  3. Q27Let $A = \{x \in N : x \text{ is a factor of } 24\}$ and $B = \{x \in N : x \text{ is a factor of } 36\}$. Find $A \cap B$ and identify its…Preview
+Show 8 questions8 questions
  1. Example 1Write the set $A = \{x : x \in N,\ x < 6\}$ in roster form.Free
  2. Example 2Write the set $B = \{5, 10, 15, 20, 25\}$ in set-builder form.Free
  3. Example 3State whether each of the following is True or False, giving a reason: (i) The set of all lines parallel to the $x$-axis is a finite set. (i…Free
  4. Example 4If $A = \{1, 2, 3, 4\}$, write the power set $P(A)$ and verify that $n(P(A)) = 2^4$.Preview
  5. Example 5Let $U = \{1, 2, 3, \dots, 10\}$, $A = \{1, 2, 3, 4, 5\}$ and $B = \{4, 5, 6, 7, 8\}$. Find $A \cup B$, $A \cap B$, $A - B$, $B - A$, $A'$,…Preview
  6. Example 6Using the sets $U$, $A$, $B$ given in Example 5, verify De Morgan's law $(A \cap B)' = A' \cup B'$.Preview
  7. Example 7Write the solution set of the inequality $-3 < x \le 7$ using interval notation, and also express it as a subset of $\mathbb{R}$ in set-buil…Preview
  8. Example 8In a survey of 50 students, 30 like tea, 25 like coffee, and 10 like both tea and coffee. Using set operations, find (i) how many students l…Preview
+Show 4 questions4 questions
  1. Q9Write the set $C = \{x : x \text{ is a prime number and } 10 < x < 30\}$ in roster form.Free
  2. Q10Write the set $D = \{1, 4, 9, 16, 25, 36\}$ in set-builder form.Free
  3. Q11Write the set $E$ of all distinct letters in the word ``MATHEMATICS'' in roster form, and state $n(E)$.Preview
  4. Q12Determine which of the following are empty sets, giving a reason in each case: (i) $\{x : x \in N \text{ and } 2x + 1 = 0\}$ (ii) $\{x : x \…Preview
+Show 3 questions3 questions
  1. Q13If $A = \{a, b, c\}$, list all the subsets of $A$ and verify that the total number of subsets is $2^3$.Free
  2. Q14If a set $A$ has 6 elements, how many elements does $P(A)$ have? How many of these are proper subsets of $A$?Preview
  3. Q15Write the following sets of real numbers as intervals: (i) $\{x \in \mathbb{R} : -4 < x < 6\}$ (ii) $\{x \in \mathbb{R} : 0 \le x < 7\}$ (ii…Preview
+Show 6 questions6 questions
  1. Q16Draw a Venn diagram for $U = \{1, 2, \dots, 10\}$, $A = \{1, 2, 3, 4\}$, $B = \{3, 4, 5, 6\}$, and shade the region representing $A \cap B$.…Free
  2. Q17If $A = \{2, 4, 6, 8, 10\}$ and $B = \{3, 6, 9, 12\}$, find $A \cup B$ and $A \cap B$.Free
  3. Q18Let $A = \{x : x \in N, x \text{ is a multiple of } 3, x \le 20\}$ and $B = \{x : x \in N, x \text{ is a multiple of } 4, x \le 20\}$. Using…Preview
  4. Q19In a group of 100 people, 72 like coffee, 60 like tea, and 40 like both. Using a Venn diagram, find how many people like coffee only, tea on…Preview
  5. Q20If $A$ and $B$ are two sets such that $A \subset B$, what are $A \cup B$ and $A \cap B$? Justify your answer with the help of a Venn diagram…Preview
  6. Q21If $A = \{a, b, c, d, e\}$ and $B = \{b, d, f, g\}$, find $A - B$ and $B - A$. What do you observe about $(A - B) \cap (B - A)$?Preview
+Show 3 questions3 questions
  1. Q22If $U = \{1, 2, \dots, 12\}$ and $A = \{2, 4, 6, 8, 10, 12\}$, find $A'$ and verify that $(A')' = A$.Free
  2. Q23If $U = \{x \in N : x \le 10\}$, $A = \{1, 2, 3, 4\}$, $B = \{2, 4, 6, 8\}$, verify De Morgan's law $(A \cup B)' = A' \cap B'$.Preview
  3. Q24Using the complement laws, simplify $A \cup A'$ and $A \cap A'$ for any subset $A$ of a universal set $U$, and state which laws these illust…Preview