Naive set theory and First-Order Logic II: Functions and Relations
Functions and relations are central to first-order logic. In fact, first-order logic is a logic designed specifically to deal with functions and relations.
First-order logic is omnipresent. Just about any statement in the English language can be written using first-order logic, from litterature papers to theoretical physics. One sees first-order logic in action every time one does a search on Google, or plays a video game.
This week we shall get acquainted with the concept of function and relations, as well as with some of the basic properties that functions and relations can have. We will also introduce the basics of first-order relational languages, and provide a rigorous definition of truth tables using first-order logic.