###### 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.