Скачать или смотреть ISC Class 11 Ch-2 Relations and Functions Ex-2.1 From ML Aggarwal Part-1

Hello Students
For any doubt u can contact me at 7009509669

ML Aggarwal's ISC Class 11, Chapter 2, "Relations and Functions," provides a comprehensive study of the mathematical relationship between sets and their elements. The chapter covers foundational concepts like the Cartesian product of sets, defines relations and their properties (domain, codomain, range), and then introduces functions as a special type of relation. It delves into various types of functions, such as one-to-one, many-to-one, onto, and real-valued functions, including their graphs, and explains how to perform operations (sum, difference, product, quotient) on them.
Key Concepts Covered
Cartesian Product of Sets: Understanding how to form ordered pairs from two non-empty sets.
Definition of a Relation: A relation is a connection between elements of two or more non-empty sets.
Domain, Codomain, and Range: Identifying the set of all first elements (domain), all potential second elements (codomain), and all actual second elements (range) in a relation or function.
Functions: A specific type of relation where each input (first element) maps to exactly one output (second element).
Types of Functions: Learning about different classifications, such as:
One-to-One Function (Injective): Each element in the domain maps to a unique element in the codomain.
Many-to-One Function: More than one element in the domain maps to the same element in the codomain.
Onto Function (Surjective): Every element in the codomain is mapped to by at least one element in the domain.
Into Function: The range is a proper subset of the codomain.
Real-Valued Functions: Functions where the domain and codomain are subsets of real numbers, including their graphical representations.
Operations on Functions: Methods for combining functions, such as finding their sum, difference, product, and quotient.
Learning Objectives
By studying this chapter, students will be able to:
Understand and apply the concept of Cartesian products for set relationships.
Distinguish between relations and functions.
Determine the domain, codomain, and range of given relations and functions.
Analyze and classify different types of functions.
Interpret and construct graphs of various real-valued functions.
Perform algebraic operations on functions