Class 11 Maths - TAMILNADU
Relations and Functions
The chapter 'Relations and Functions' in Class 11 Mathematics under the Tamil Nadu Samacheer Kalvi syllabus builds a strong foundation for higher-level mathematics. It introduces students to the fundamental concepts of ordered pairs, Cartesian products of sets, and how elements of sets are associated with each other. You will learn to distinguish between general relations and specific functions, explore various types of functions like real-valued functions, polynomial, rational, modulus, and greatest integer functions, and understand their graphical representations. Mastering this chapter is essential for scoring well in board exams and forms the basis for calculus and advanced algebra in Class 12.
Start Learning FreeKey Concepts
Cartesian Product
The Cartesian product of two non-empty sets A and B, denoted by A × B, is the set of all ordered pairs (a, b) such that a belongs to A and b belongs to B.
Relation
A relation R from a non-empty set A to a non-empty set B is a subset of the Cartesian product A × B, established by a specific rule connecting the elements.
Function
A relation f from a set A to a set B is called a function if every element in set A has one and only one image in set B.
Domain, Co-domain and Range
For a function f: A → B, set A is the domain, set B is the co-domain, and the set of all actual outputs (images) in B is the range.
Types of Functions
Functions are classified based on their mapping properties into one-to-one (injective), onto (surjective), and bijective functions, along with special functions like identity, constant, and modulus functions.
Important Formulas
Board Exam Info
In the Tamil Nadu (Samacheer Kalvi) Class 11 Mathematics public examination, this chapter typically carries around 8 to 12 marks. Questions commonly appear in 1-mark (MCQs), 2-mark, 3-mark, and 5-mark sections. Expect graphical representation of functions, finding the domain and range of real functions, and problems based on Cartesian products and types of relations.
Frequently Asked Questions
What is the difference between a relation and a function?
Every function is a relation, but not every relation is a function. In a relation, an input can have multiple outputs. In a function, every input must have a unique and single output.
How do I find the domain and range of a function?
The domain is the set of all possible input values (x) for which the function is defined. The range is the set of all resulting output values [f(x)] obtained when substituting the domain values.
How many relations can be formed from set A to set B?
If set A has p elements and set B has q elements, the total number of subsets in A × B is 2^(pq), which is the total number of possible relations.
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