In the world of business and IT, clear thinking and sound reasoning are essential. Whether you’re designing a database, writing code, analyzing data, or making strategic decisions, you’re constantly working with logic, even if you don’t always realize it. In this chapter, the principles of mathematical logic and proof will be introduced to you, providing you with a foundation for understanding how computers can “think”.

We’ll start by looking at propositions, which are the basic units of logic that represent true/false conditions used in programming and decision-making. Just like optimizing business logic in software or spreadsheets, we’ll then look at how to simplify complicated rules using conditional statements and logical equivalence. Next, we’ll introduce quantifiers, which allow us to express statements about entire sets (like filters in a database query). Debugging or validating a business rule is also important, and we’ll learn how to do this by covering mathematical induction, a powerful method for proving patterns and processes that repeat, much like loops in programming or trends in business forecasting.