🧠 Test 4 – Formal Logic

📅 Test Details

📚 Topics Covered

• Propositional logic (syntax and semantics)
• Natural deduction proofs
• Logical equivalence and consequence
• Predicate logic basics
• Quantifiers (universal and existential)
• Categorical logic and syllogisms

🎯 Sample Problem Types

• Tautologies: Determine if given formula is a tautology
• Proofs: Prove arguments using natural deduction
• Equivalence: Show logical equivalences using truth tables
• Translation: Translate English sentences to predicate logic
• Validity: Determine if arguments are valid
• Syllogisms: Analyze classical syllogisms

📖 Preparation Guide

Review Materials

1. Lecture Notes: Module 4 (Formal Logic)
2. Homework: HW 4
3. Textbook: Kenneth Rosen

Practice Problems

• Tautologies: Test 10–15 formulas using truth tables
• Proofs: Complete natural deduction proofs for common theorems
• Equivalences: Show logical equivalence for 5–10 pairs
• Translation: Convert 20+ English sentences to predicate logic
• Quantifiers: Negate complex quantified formulas
• Syllogisms: Analyze validity of classical argument forms

Common Pitfalls

⚠️ Watch Out!

• Quantifier negation: \( \neg \forall x ~ P(x) \) means “there exists \(x\) such that \( \neg P(x) \)”
• Scope matters in predicate logic
• In proofs: justify every step with a rule name
• Translation: “only” is not the same as “all” (contrapositive!)
• Syllogisms: check for fallacies (undistributed middle, etc.)

💡 Pro Tips

• Truth tables work – when unsure about tautology, build the table
• Proof strategy – work backwards from conclusion to find needed steps
• Name your rules – explicitly cite modus ponens, ∧-intro, etc.
• Quantifier scope – use parentheses to clarify scope clearly
• Practice translation – “all”, “some”, “no”, “only” have precise meanings
• Check validity – valid argument = impossible for premises true and conclusion false