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NCERT Solutions for Class 11 Math Ch-1: Sets
NCERT Solutions for Class 11 Maths Chapter 1 Sets covers the definition and representation of sets, types of sets, operations on sets such as union and intersection, and Venn diagrams.
Overview of Topics & Subtopics
Important Questions and Answers
Q1: What is a set, and what are the two common methods of representing a set?
Answer: A set is a well-defined collection of distinct objects, called elements. The two common methods of representation are the Roster (or tabular) form, where elements are listed within curly braces, e.g., {2, 4, 6, 8}, and the Set-Builder form, where elements are described by a common property, e.g., {x : x is an even natural number less than 10}.
Q2: Define a subset and a power set.
Answer: A set A is called a subset of set B if every element of A is also an element of B, denoted A ⊆ B. The power set of a set A is the set of all possible subsets of A, including the empty set and A itself, denoted P(A).
Q3: What is the difference between the union and intersection of two sets?
Answer: The union of two sets A and B (A ∪ B) is the set containing all elements that are in A, in B, or in both. The intersection of two sets A and B (A ∩ B) is the set containing only the elements that are common to both A and B.
Q4: Define the complement of a set.
Answer: The complement of a set A, denoted A′, with respect to a universal set U, is the set of all elements in U that are not in A, i.e., A′ = U − A.
Q5: State the formula used to find the number of elements in the union of two sets.
Answer: For two finite sets A and B, the number of elements in their union is given by n(A ∪ B) = n(A) + n(B) − n(A ∩ B), which accounts for elements common to both sets being counted only once.
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