Exercises of Sets and Functions E-Book

Simone Malacrida

• Herausgeber: Simone Malacrida
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Veröffentlichungsjahr: 2022

Beschreibung

In this book, exercises are carried out regarding the following mathematical topics:
set theory
functions and properties of functions
Initial theoretical hints are also presented to make the performance of the exercises understandable

Leseprobe

Table of Contents

"Exercises of Sets and Functions"

INTRODUCTION

THEORETICAL OUTLINE

EXERCISES

"Exercises of Sets and Functions"

SIMONE MALACRIDA

In this book, exercises are carried out regarding the following mathematical topics:

set theory

functions and properties of functions

Initial theoretical hints are also presented to make the performance of the exercises understandable

Simone Malacrida (1977)

Engineer and writer, has worked on research, finance, energy policy and industrial plants.

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ANALYTICAL INDEX

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INTRODUCTION

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I – THEORETICAL OUTLINE

Sets

Functions

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II – EXERCISES

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

Exercise 7

Exercise 8

Exercise 9

Exercise 10

Exercise 11

Exercise 12

Exercise 13

Exercise 14

Exercise 15

INTRODUCTION

In this workbook, some examples of calculus relating to sets and functions are carried out.

In order to understand in more detail what is presented in the resolution of the exercises, the theoretical reference context is recalled in the first chapter.

What is presented in this workbook is generally addressed at the high school level during a course that covers several years.

I

THEORETICAL OUTLINE

Sets

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We define the primitive and intuitive concept of mathematical set as a collection of objects, called elements , indicated with lowercase letters, while sets with uppercase letters.

If an element belongs to a given set, it is indicated with the logical symbol of belonging.

Two sets coincide if and only if they have the same elements.

A set is said to be finite if it has a finite number of elements, conversely it is said to be infinite.

The number of elements of a finite set is called cardinality and is denoted by card(A).

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On sets you can perform the logical operations of union, intersection and negation.

Union corresponds to inclusive disjunction, while intersection to logical conjunction.

We can also define the difference between set B and set A in the same way as we define the difference of two numbers.

We define the Cartesian product as the set of all possible ordered pairs (a,b) with a belonging to set A and b to set B.

The Cartesian product looks like this: