Relations and Functions — Chapter Summary
Tamil Nadu Board · Class 10 · Mathematics
Summary of Relations and Functions for Tamil Nadu Board Class 10 Mathematics. Part of the Tamil Nadu Board Class 10 Mathematics syllabus.
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Overview
Relations and Functions are fundamental concepts in mathematics that help us understand how different objects or quantities are connected to each other. A relation describes a connection between elements of two sets, while a function is a special type of relation where each input has exactly one out
Key Concepts
An ordered pair consists of two
An ordered pair consists of two elements written in a specific order, denoted as (a, b). The order matters—(3, 5) is different from (5, 3). Ordered pa
The Cartesian product of two non
The Cartesian product of two non-empty sets A and B, denoted A × B, is the set of all ordered pairs (a, b) where a ∈ A and b ∈ B. If A = {1, 2} and B
A relation R from set
A relation R from set A to set B is any subset of A × B. It connects elements from A to elements in B according to some rule. For example, if A = {1,
For a relation R from
For a relation R from A to B: Domain = set of all first elements that actually appear in R (subset of A); Co-domain = set B (specified at the start);
A function f from set
A function f from set A to set B is a special relation where every element in A has exactly one image in B. It's a 'rule' that takes an input from A a
Learning Objectives
- Understand and apply the concept of Cartesian product of sets
- Define relations as subsets of Cartesian products and identify their domain, co-domain, and range
- Distinguish between relations and functions, understanding that every function is a relation but not vice versa
- Represent functions using multiple methods: arrow diagrams, ordered pairs, tables, rules, and graphs
- Classify functions into types: one-one (injective), many-one, onto (surjective), into, and bijective functions
Frequently Asked Questions
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Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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