Chapter Three Functions 3.1 PDF
Document Details
Uploaded by EnviousCourage
Tags
Related
- FY BSc Algebra NEP2-24-25 Theory PDF
- Discrete Mathematics (210241) Savitribai Phule Pune University PDF
- Mathematics for Natural Sciences PDF
- Basic Structures: Sets, Functions, Sequences, Sums, & Matrices Chapter 2 PDF
- Appunti di Analisi Matematica I - A.S. 2021-2022 PDF
- Matemática Discreta Past Paper PDF
Summary
This document details functions, specifically the Cartesian product of sets, which are key concepts in set theory. The example provided demonstrates the creation of ordered pairs and subsets of Cartesian products.
Full Transcript
Chapter Three Functions 3.1 Definition 3.1.1 Suppose A and B are sets. The Cartesian product of A and B , denoted by A × B is the set which contains every ordered pair whose first coordinate is an element of A and second coordinate is an element of B , i.e. A × B = {(a, b) : a...
Chapter Three Functions 3.1 Definition 3.1.1 Suppose A and B are sets. The Cartesian product of A and B , denoted by A × B is the set which contains every ordered pair whose first coordinate is an element of A and second coordinate is an element of B , i.e. A × B = {(a, b) : a ∈ A and b ∈ B} Example 3.1.1 For A = {2, 4} and B = {−1, 3} , we have a) A × B = {(2, −1), (2, 3), (4, −1), (4, 3)} and b) B × A = {(−1, 2), (−1, 4), (3, 2), (3, 4)} Definition 3.1.2 If A and B are sets, any subset of A × B is called a relation from A into B. () March 21, 2023 2/2
