Exam Unit 1 Topic List.docx

Course: Geometry Teacher: Mr. Cervone ***List of Topic for Exam Unit 1*** ------------------ **TOPIC: LOGIC** ------------------ **1. Introduction to Logic** [Mathematical Sentences ] Nonmathematical Sentences Open Sentences (identify variable) Closed Sentences **2. [Negation ]...

Course: Geometry Teacher: Mr. Cervone ***List of Topic for Exam Unit 1*** ------------------ **TOPIC: LOGIC** ------------------ **1. Introduction to Logic** [Mathematical Sentences ] Nonmathematical Sentences Open Sentences (identify variable) Closed Sentences **2. [Negation ]** Symbol: \~ **3. [Conjunctions (And) ]** Symbol: ∧ Truth Table: **p** **q** **p** ∧ **q** ------- ------- --------------- T F F F T F F F F **4. [Disjunctions (Or) ]** Symbol: ∨ Truth Table: **p** **q** **p** ∨ **q** ------- ------- --------------- T F F T F F F **5. [Conditionals (If..., then...) ]** Symbol: → Truth Table: **p** **q** **p** → **q** ------- ------- --------------- T F F F T F F **6. [Biconditionals (...if and only if...) ]** Symbol: ↔ Truth Table: **p** **q** **p** ↔ **q** ------- ------- --------------- T F F F T F F F **7. [Tautology]** Compound sentence that is always true (T) **8. [Logically Equivalent Statements ]** **9. [De Morgan's Law ]** Premise: \~(p ∧ q) Conclusion: ∴\~p∨ \~q Premise: \~(p∨ q) Conclusion: ∴\~p ∧ \~q **10. [Conditional, Converse, Inverse,]** **[Contrapositive ]** Conditional: p →q Converse: q→p Inverse: \~p →\~q Contrapositive: \~q →\~p Conditionals and Contrapositives are logically equivalent: (p →q) ↔(\~q →\~p) **11. [Law of Contrapositives ]** Premise: p → q Conclusion: ∴ \~q →\~p **12. [Law of Modus Ponens (Law of Detachment])** Premise: p → q Premise: p Conclusion: ∴q Page \| **1** Course: Geometry Teacher: Mr. Cervone **13. [Law of Modus Tollens ]** Premise: p → q Premise: \~q Conclusion: ∴\~p **14. [Law of Disjunctive Inference ]** Premise: p ∨ q Premise: \~p Conclusion: ∴q Premise: p ∨ q Premise: \~q Conclusion: ∴p **15. Law of Conjunction** Premise: p Premise: q Conclusion: ∴ p ∧ q **16. Law of Simplification** Premise: p ∧ q Conclusion: ∴p Premise: p ∧ q Conclusion: ∴q **17. Law of Disjunctive Addition** Premise: p Conclusion: ∴p∨ q **18. [Chain Rule (Law of Syllogism) ]** Premise: p → q Premise: q → r Conclusion: ∴p →r **19. Law of Double Negation** Premise: \~(\~p) Conclusion ∴p **20.** Logic Proofs **21.** Indirect Logic Proofs Page \| **2**