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Class 11 Math Ch-2: Relations and Functions Notes
Class 11 Maths Chapter 2 Relations and Functions introduces the concept of ordered pairs, Cartesian products, relations between sets, and functions along with their domain, codomain, and range.
Overview of Topics & Subtopics
Important Questions and Answers
Q1: What is the Cartesian product of two sets A and B?
Answer: The Cartesian product of two sets A and B, denoted A × B, is the set of all possible ordered pairs (a, b) such that a belongs to A and b belongs to B; if A has m elements and B has n elements, then A × B has mn elements.
Q2: Define a relation from set A to set B.
Answer: A relation R from a non-empty set A to a non-empty set B is defined as any subset of the Cartesian product A × B; it describes an association between elements of A and elements of B.
Q3: What is the difference between the domain, codomain, and range of a relation or function?
Answer: The domain is the set of all first elements (inputs) of the ordered pairs in the relation. The codomain is the entire set B, the target set to which elements are mapped. The range is the set of all actual second elements (outputs) obtained from the relation, and it is always a subset of the codomain.
Q4: What condition must a relation satisfy to be classified as a function?
Answer: A relation from set A to set B is called a function if every element of set A has one and only one image in set B, meaning no element of the domain maps to more than one element in the codomain.
Q5: Define the modulus function and state its domain and range.
Answer: The modulus function is defined as f(x) = |x|, which equals x if x ≥ 0, and equals −x if x < 0. Its domain is the set of all real numbers (R), and its range is the set of all non-negative real numbers [0, ∞).
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