MATH 280 Discrete Mathematical Structures Test 2 Study Guide

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