1: Mathematics and Problem-Solving

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We are surrounded by information—information in various forms such as numbers, charts, graphs, figures, sentences, songs, speeches, and conversations. Much of the information comes through media including television, magazines, and online communications. Many of the things we hear and read are true while many are not. How are we to determine what is true and what is not? What is truth anyway? Are there ways to detect false information? What are we to watch out for?

One of the primary goals of this book is to answer some of these questions through logic and mathematics. This is particularly important in the Internet-dominated, media-centered, and information-driven age in which we find ourselves living today. With new technologies, it is becoming much easier for businesses and organizations to send out deceptive messages and misleading advertisements, and they can target specific individuals based on their online activities. Throughout this book you will find data, numbers, and statements that can be presented honestly or dishonestly in a deceptive manner. They may be numbers, percentages, odds, statistics, or written sentences.

In this first chapter we study logic, both correct use of logic and logical fallacies. Before we get into the formal side of logic, however, we first look at some types of fallacies presented as English sentences. In other words, we will see some bad examples of logical arguments presented in common language. Then, in the following sections we will look carefully into some formal components of logic like propositions, truth tables, and logical equivalences.

Contributors and Attributions

Saburo Matsumoto
CC-BY-4.0