Test 1: Set Theory

Week: 3
Coverage: Weeks 1-2
Duration: 90 minutes

Topics Covered

• Set operations (∪, ∩, , ⊖, complement)
• Venn diagrams
• Power sets
• Cardinality of finite sets
• Cartesian products
• Set identities and proofs

Sample Problem Types

1. Operations: Given sets A, B, C, compute A ∪ (B \ C)
2. Venn diagrams: Draw diagram for (A ∩ B) ∪ (A ∩ C)
3. Proofs: Prove A \ (B ∪ C) = (A \ B) ∩ (A \ C)
4. Power sets: Find |𝒫(A)| for given A
5. Cartesian products: Determine A × B for specific sets

Key Skills

• Fluency with set notation
• Visual reasoning (Venn diagrams)
• Proof techniques (element method, double inclusion)
• Understanding power sets
• Cartesian product calculations

Preparation

• Review Lecture 1 notes
• Rework Homework 1 problems
• Practice textbook exercises (Rosen Ch 2.1-2.2)
• Create formula/identity reference sheet