The material presented in this guide covers the concepts emphasized on the final examination. It is meant to guide students studying and reviewing for the final exam; it is not guaranteed to be comprehensive. Actual test questions will differ from the examples given here. Students should use this guide in addition to other study activities (like re-reading Chapters 4–6, reviewing completed assignments, quizzes, etc.)

Things to know:

- Sets and Logic
- Definition of set operations using the notation of mathematical logic
- Proof of a law of set theory (Example: Prove the associative law of set theory for intersection using the logic laws and inference rules from Chapter 3)
- Duality

- Matrix Algebra:
- Order of a matrix
- Matrix addition
- Scalar multiplication
- Matrix multiplication
- Identity matrices
- Laws of matrix algebra

- Relations:
- representing with directed graphs
- properties (reflexive, symmetric, antisymmetric, transitive),
- partially ordered sets (Hasse diagrams, minimal and maximal elements)
- equivalence relations (set partitioning)
- transitive closure