$\newcommand{\identity}{\mathrm{id}} \newcommand{\notdivide}{\nmid} \newcommand{\notsubset}{\not\subset} \newcommand{\lcm}{\operatorname{lcm}} \newcommand{\gf}{\operatorname{GF}} \newcommand{\inn}{\operatorname{Inn}} \newcommand{\aut}{\operatorname{Aut}} \newcommand{\Hom}{\operatorname{Hom}} \newcommand{\cis}{\operatorname{cis}} \newcommand{\chr}{\operatorname{char}} \newcommand{\Null}{\operatorname{Null}} \newcommand{\transpose}{\text{t}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \setcounter{chapter}{-1}$

# Section30 Preliminaries: Preparation

###### ObjectivesLearning Goals for this Chapter
• Write a proof that follows a clear, appropriate logical form of argument (direct, contraposition, contrapositive).
• State and understand the three properties that make a relation an equivalence relation.
• Describe the partition of a set defined by a given equivalence relation.
• Perform arithmetic with residues modulo $n\text{.}$
• State precisely the definitions of one-to-one, onto, associativity, and inverse for functions.

This chapter is intended to refresh your skills in working with sets and writing clearly and logically-structured proofs. We will draw upon these skills consistently throughout the semester, so now is the time to brush up on them before new material competes for your attention!