Formal Logic and Proofs by Truth Tables

We will be interested in arguments about mathematical structures and mathematical proofs throughout the book so that we can establish mathematical truths that will be used in practical problems. For this reason, in this section, we wish to establish some familiarity with the strict logic required to establish some mathematical theory that allows us to solve practical mathematical problems.

The foundation of all mathematics is logic, which studies how we can construct logically sound arguments that show that certain assumptions lead to certain conclusions with no doubt. In particular, formal logic abstracts away any specifics of the particular arguments being constructed in order to focus on the structure of the arguments, which can establish some general principles or shortcuts that can be used in specific arguments. Aristotle developed many principles of syllogistic logic, which is logic focusing on arguments that deductively lead from some...