Test 2: Binary Relations

Week: 7
Coverage: Weeks 3-7
Duration: 90 minutes

Topics Covered

• Relation properties (reflexive, symmetric, transitive, etc.)
• Equivalence relations and partitions
• Order relations and Hasse diagrams
• Functions (injective, surjective, bijective)
• Composition
• Cardinality (finite, countable, uncountable)

Sample Problem Types

1. Properties: Determine which properties R satisfies
2. Equivalence classes: Find equivalence classes for given relation
3. Hasse diagrams: Draw diagram for partial order
4. Functions: Prove f is bijective
5. Composition: Compute f ∘ g
6. Cardinality: Show set is countable/uncountable

Key Skills

• Classifying relations
• Working with equivalence classes
• Drawing Hasse diagrams
• Analyzing functions
• Composing correctly
• Cardinality arguments

Preparation

• Review Lectures 2-4 notes
• Rework Homework 2 problems
• Practice Hasse diagram construction
• Review cardinality proofs