FUZY MATH ACADEMY

Class 11 Maths Chapter 1 Sets – Exercise 1.6 NCERT Solutions Introduction Exercise 1.6 focuses on algebra of sets. Students learn how to apply set identities such as distributive laws, De Morgan’s laws, and verify relations using Venn diagrams. This exercise strengthens logical reasoning and prepares students for probability and relations. Key Concepts Distributive Laws: A ∩ ( B ∪ C ) = ( A ∩ B ) ∪ ( A ∩ C ) A ∪ ( B ∩ C ) = ( A ∪ B ) ∩ ( A ∪ C ) De Morgan’s Laws: ( A ∪ B ) ′ = A ′ ∩ B ′ ( A ∩ B ) ′ = A ′ ∪ B ′ Idempotent Laws: A ∪ A = A , A ∩ A = A Complement Laws: A ∪ A ′ = U , A ∩ A ′ = ∅ Common Mistakes Forgetting to apply distributive property correctly. Misinterpreting complement relative to universal set. Confusing union with intersection in De Morgan’s laws. Ignoring boundary cases like empty set or universal set. NCERT Questions with Step‑by‑Step Solutions (10) Q1. Verify: A ∪ ( B ∩ C ) = ( A ∪ B ) ∩ ( A ∪ C ) . Using distributive law, both sides are equal. Verified. Q2. Ver...

Class 11 Maths Chapter 1 Sets – Exercise 1.5 NCERT Solutions Introduction Exercise 1.5 focuses on practical problems on sets. Students learn how to apply set operations to real‑life situations, including union, intersection, and complement of sets. This exercise strengthens problem‑solving skills and prepares students for probability and relations. Key Concepts Union of Sets: A ∪ B = { x : x ∈ A  or  x ∈ B } Intersection of Sets: A ∩ B = { x : x ∈ A  and  x ∈ B } Complement of a Set: A ′ = { x : x ∉ A } Cardinality Relation: n ( A ∪ B ) = n ( A ) + n ( B ) − n ( A ∩ B ) Common Mistakes Forgetting to subtract intersection when calculating union. Misinterpreting complement as difference. Confusing universal set with given set. Ignoring overlapping elements in Venn diagrams. NCERT Questions with Step‑by‑Step Solutions (10) Q1. In a group of 70 students, 30 like cricket, 20 like football, and 35 like hockey. 5 like all three. Find how many like at least one game. n ( C ∪...

Class 11 Maths Chapter 1 Sets – Exercise 1.3 NCERT Solutions Introduction Exercise 1.3 focuses on Venn diagrams and set identities. You will learn how to represent sets graphically, verify identities, and solve problems using union, intersection, difference, and complement. These concepts are widely applied in logic, probability, and computer science. Formula Used Union: A ∪ B = { x : x ∈ A  or  x ∈ B } Intersection: A ∩ B = { x : x ∈ A  and  x ∈ B } Difference: A − B = { x : x ∈ A  and  x ∉ B } Complement: A ′ = { x : x ∈ U  and  x ∉ A } Key Identities: A ∪ A ′ = U A ∩ A ′ = ∅ ( A ∪ B ) ′ = A ′ ∩ B ′ ( A ∩ B ) ′ = A ′ ∪ B ′ NCERT Questions with Solutions (10) Q1. Verify A ∪ A ′ = U . Since every element is either in A or not in A , A ∪ A ′ = U Q2. Verify A ∩ A ′ = ∅ . No element can be both in A and not in A . A ∩ A ′ = ∅ Q3. Verify De Morgan’s law: ( A ∪ B ) ′ = A ′ ∩ B ′ . Using Venn diagram, shaded regions match. Q4. Verify De Morga...

Class 11 Maths Chapter 1 Sets – Exercise 1.2 NCERT Solutions Introduction Exercise 1.2 focuses on operations on sets such as union, intersection, difference, and complement. These operations are fundamental in set theory and are widely applied in mathematics, computer science, and logic. Formula Used Union of sets: A ∪ B = { x : x ∈ A  or  x ∈ B } Intersection of sets: A ∩ B = { x : x ∈ A  and  x ∈ B } Difference of sets: A − B = { x : x ∈ A  and  x ∉ B } Complement of set: A ′ = { x : x ∈ U  and  x ∉ A } Where U is the universal set. NCERT Questions with Solutions (10) Q1. If A = { 1 , 2 , 3 } , B = { 2 , 3 , 4 } , find A ∪ B . A ∪ B = { 1 , 2 , 3 , 4 } Q2. If A = { 1 , 2 , 3 } , B = { 2 , 3 , 4 } , find A ∩ B . A ∩ B = { 2 , 3 } Q3. If A = { 1 , 2 , 3 } , B = { 2 , 3 , 4 } , find A − B . A − B = { 1 } Q4. If A = { 1 , 2 , 3 } , B = { 2 , 3 , 4 } , find B − A . B − A = { 4 } Q5. If U = { 1 , 2 , 3 , 4 , 5 } , A = { 1 , 2 , 3 } , find A ′ . A ′ =...

Class 11 Maths Chapter 1 Sets – Exercise 1.1 NCERT Solutions Introduction Exercise 1.1 introduces the fundamental concepts of sets. A set is a well‑defined collection of distinct objects. You will learn how to represent sets, identify elements, and distinguish between finite, infinite, empty, singleton, and equal sets. This exercise builds the foundation for advanced set operations. Key Definitions Set: A collection of distinct objects. Element: Each object in a set. Empty Set ( ∅ ): A set with no elements. Finite Set: A set with countable elements. Infinite Set: A set with uncountable elements. Singleton Set: A set with exactly one element. Equal Sets: Two sets with exactly the same elements. Subset: If every element of A is in B , then A ⊆ B . NCERT Questions with Solutions (10) Q1. Which of the following are sets? Justify. Examples: collection of vowels in English alphabet, collection of good students in a class. Vowels = { a , e , i , o , u } → well‑defined, hence a set...

Class 11 Maths Chapter 2 Relations and Functions – Exercise 2.3 NCERT Solutions Introduction Exercise 2.3 introduces the concept of functions as special types of relations. A function maps each element of the domain to exactly one element of the codomain. You will learn how to identify functions, determine their domain and range, and classify them as one‑one or onto. Key Definitions Function: A relation f : A → B is a function if every element of A is related to exactly one element of B . Domain: Set of all first elements of ordered pairs. Range: Set of all second elements actually mapped. Codomain: The target set B . One‑One Function (Injective): Different elements of domain map to different elements of codomain. Onto Function (Surjective): Every element of codomain has a pre‑image in domain. NCERT Questions with Solutions (10) Q1. Check if relation f : A → B defined by f ( x ) = x 2 , A = { 1 , 2 , 3 } , B = { 1 , 4 , 9 } is a function. Yes, each x ∈ A maps to ex...

Class 11 Maths Chapter 2 Relations and Functions – Exercise 2.2 NCERT Solutions Introduction Exercise 2.2 focuses on types of relations such as reflexive, symmetric, and transitive relations. You will learn how to check whether a given relation satisfies these properties and how to classify relations accordingly. These concepts are foundational for understanding equivalence relations and functions. Key Definitions Reflexive Relation: A relation R on set A is reflexive if ( a , a ) ∈ R for all a ∈ A . Symmetric Relation: A relation R on set A is symmetric if ( a , b ) ∈ R    ⟹    ( b , a ) ∈ R . Transitive Relation: A relation R on set A is transitive if ( a , b ) ∈ R , ( b , c ) ∈ R    ⟹    ( a , c ) ∈ R . Equivalence Relation: A relation that is reflexive, symmetric, and transitive. NCERT Questions with Solutions (10) Q1. Show that relation R on set A = { 1 , 2 , 3 } defined by R = { ( 1 , 1 ) , ( 2 , 2 ) , ( 3 , 3 ) } is reflexive. Since ( a , a ) ∈ R for a...