Mathematics in Cybersecurity

2Logic

2.1 Introduction to Logic

Logic is a fundamental branch of mathematics that deals with the study of reasoning, inference, and the principles of valid arguments. It provides a framework for analyzing and evaluating the correctness of assertions, statements, and proofs.

In this section, we explore the definition of logic, its importance in discrete mathematics, and the basic building blocks of logical reasoning: propositions and logical connectives.

2.1.1 Definition of Logic

Logic is the study of the principles and methods of reasoning, particularly in the context of mathematical and philosophical arguments. Arguments are a set of statements (two or more premises and a conclusion), and one of the objectives of logic is to determine if a particular argument is valid—we distinguish between the notions of validity and soundness, which we will discuss shortly.

The premises purportedly provide evidence, reasons, and grounds for the conclusion, which is the notion for which the argument is being made. An argument alleges some reasoned connection between the premises and the conclusion, and such a connection is the subject of logical analysis.

The study of logic involves the systematic analysis of the form and structure of arguments, rather than the content of those arguments. The validity of arguments is based on the correctness of their logical form, independent of the truth or falsity of their premises. A premise is a proposition antecedently supposed in an argument; for ...