📐 Test 1 – Set Theory

📅 Test Details

📚 Topics Covered

• Set operations (union, intersection, difference, symmetric difference, complement)
• Venn diagrams
• Power sets
• Cardinality
• Cartesian products
• Set identities (De Morgan’s, distributive, etc.)
• Basic proofs with sets

🎯 Sample Problem Types

• Operations: Compute set expressions
• Venn Diagrams: Draw and shade regions for given formulas
• Proofs: Prove set identities using element method
• Power Sets: Calculate power set size for given set
• Cartesian Products: Find Cartesian products for specific sets
• Cardinality: Apply inclusion-exclusion principle

📖 Preparation Guide

Review Materials

1. Lecture Notes: Module 1 (Set Theory)
2. Homework: HW 1
3. Textbook: Kenneth Rosen

Practice Problems

• Basic: All set operations on 2–3 sets
• Venn Diagrams: Shade regions for complex expressions
• Proofs: Element method for 5–10 identities
• Power Sets: Calculate for sets of size 0–5
• Products: Cartesian products with different cardinalities

Common Pitfalls

⚠️ Watch Out!

• Don’t confuse “element of” with “subset of”
• Remember: set difference is not commutative
• Power set of empty set has one element (the empty set itself)
• Venn diagrams: label all regions clearly

💡 Pro Tips

• Show all work – even for “obvious” set operations
• Use element method – “let \(x \in A\)…” is your friend
• Draw diagrams – Venn diagrams help verify your work
• Check edge cases – test with empty set, singletons
• Double-check notation – { } vs ( ) matters!