Description

This is a study guide to help you prepare for the exam. While it aims to be comprehensive, it is not guaranteed to cover every topic that may appear on the exam. It is important to review all of your notes and the course materials.

Questions

1. Identify the premises of this sequent: ¬(A ↔︎ C), B ∨ D, ¬D ⊢ ¬(A → E) (question id 05_pl_setup_23)
2. Identify which rule is used in the following: M ∧ N ⊢ M (question id 05_pl_proofs_firstfour_17)
3. Identify which rule is used in the following: ¬A, B ⊢ ¬A ∧ B (question id 05_pl_proofs_firstfour_35)
4. Identify which rule is used in the following: ¬D → E, ¬D ⊢ E (question id 05_pl_proofs_firstfour_71)
5. Identify which rule is used in the following: Assume S ∧ U, derive T in the subproof, and finally derive (S ∧ U) → T from the subproof starting with S ∧ U and ending with T (question id 05_pl_proofs_firstfour_118)
6. Identify which rule is used in the following: ¬P ∧ Q ⊢ ¬P (question id 05_pl_proofs_intelim_23)
7. Identify which rule is used in the following: P, Q ⊢ P ∧ Q (question id 05_pl_proofs_intelim_53)
8. Identify which rule is used in the following: P → ¬Q, P ⊢ ¬Q (question id 05_pl_proofs_intelim_92)
9. Identify which rule is used in the following: Assume D ∧ F, derive E in the subproof, and finally derive (D ∧ F) → E from the subproof starting with D ∧ F and ending with E (question id 05_pl_proofs_intelim_108)
10. Identify which rule is used in the following: M ⊢ M (question id 05_pl_proofs_intelim_133)
11. Identify which rule is used in the following: Assume J, derive K and ¬(K). From this subproof, derive ¬(J). (question id 05_pl_proofs_intelim_151)
12. Identify which rule is used in the following: Assume ¬(M), derive N and ¬(N). From this subproof, derive M. (question id 05_pl_proofs_intelim_169)
13. Identify which rule is used in the following: ¬A ⊢ ¬A ∨ B (question id 05_pl_proofs_intelim_179)
14. Identify which rule is used in the following: From S ∨ (T ∧ ¬U), assume S and derive U in the subproof, then separately assume T ∧ ¬U and derive U in that subproof. Finally, finally derive U (question id 05_pl_proofs_intelim_222)
15. Identify which rule is used in the following: A ↔︎ B, A ⊢ B (question id 05_pl_proofs_intelim_225)
16. Identify which rule is used in the following: Assume J then derive K. Next, assume K and derive K. From these two subproofs, derive the biconditional J ↔︎ K. (question id 05_pl_proofs_intelim_255)
17. Identify which rule is used in the following: (P ∨ R) ∧ Q ⊢ P ∨ R (question id 05_pl_proofs_all_24)
18. Identify which rule is used in the following: ¬S, (T → U) ⊢ ¬S ∧ (T → U) (question id 05_pl_proofs_all_60)
19. Identify which rule is used in the following: (A ∨ ¬B) → (C ∨ B), (A ∨ ¬B) ⊢ C ∨ B (question id 05_pl_proofs_all_69)
20. Identify which rule is used in the following: Assume P, derive Q in the subproof, and finally derive P → Q from the subproof starting with P and ending with Q (question id 05_pl_proofs_all_115)
21. Identify which rule is used in the following: ¬S ⊢ ¬S (question id 05_pl_proofs_all_140)
22. Identify which rule is used in the following: Assume P, derive Q and ¬(Q). From this subproof, derive ¬(P). (question id 05_pl_proofs_all_155)
23. Identify which rule is used in the following: Assume ¬(D → E), derive F and ¬(F). From this subproof, derive D → E. (question id 05_pl_proofs_all_164)
24. Identify which rule is used in the following: M → O ⊢ (M → O) ∨ ¬N (question id 05_pl_proofs_all_196)
25. Identify which rule is used in the following: From M ∨ (N ∧ ¬O), assume M and derive O in the subproof, then separately assume N ∧ ¬O and derive O in that subproof. Finally, finally derive O (question id 05_pl_proofs_all_218)
26. Identify which rule is used in the following: V ↔︎ W, V ⊢ W (question id 05_pl_proofs_all_246)
27. Identify which rule is used in the following: Assume S then derive T ∧ U. Next, assume T ∧ U and derive T. From these two subproofs, derive the biconditional S ↔︎ (T ∧ U). (question id 05_pl_proofs_all_262)
28. Identify which rule is used in the following: ¬J → K, ¬K ⊢ ¬¬J (question id 05_pl_proofs_all_275)
29. Identify which rule is used in the following: M ∨ N, ¬M ⊢ N (question id 05_pl_proofs_all_301)
30. Identify which rule is used in the following: ¬V → W, W → X ⊢ ¬V → X (question id 05_pl_proofs_all_335)
31. Identify which rule is used in the following: J ⊢ ¬¬J (question id 05_pl_proofs_all_346)
32. Identify which rule is used in the following: ¬(G ∧ H) ⊢ ¬G ∨ ¬H (question id 05_pl_proofs_all_369)
33. Identify which rule is used in the following: G → H ⊢ ¬G ∨ H (question id 05_pl_proofs_all_399)
34. Identify which PL rule is used in the following pseudo-English argument: not-A and not-Q. Therefore not-Q. (question id 05_pl_proofs_pseudo_4)
35. Identify which PL rule is used in the following pseudo-English argument: A or B. not-Z. Therefore, (A or B) and not-Z. (question id 05_pl_proofs_pseudo_9)
36. Identify which PL rule is used in the following pseudo-English argument: If not both (A and B), then W. not both (A and B). Therefore, W. (question id 05_pl_proofs_pseudo_16)
37. Identify which PL rule is used in the following pseudo-English argument: Assume not-A and derive Z within that subproof. Finally, derive if not-Z, then Z. (question id 05_pl_proofs_pseudo_18)
38. Identify which PL rule is used in the following pseudo-English argument: Assume W or S (creating a subproof) and derive S and not-S within that subproof. Finally, derive not (W or S). (question id 05_pl_proofs_pseudo_23)
39. Identify which PL rule is used in the following pseudo-English argument: Assume not (W and M) (creating a subproof) and derive P and not-P within that subproof. Finally, derive W and M. (question id 05_pl_proofs_pseudo_28)
40. Identify which PL rule is used in the following pseudo-English argument: P or S. Therefore (P or S) or M. (question id 05_pl_proofs_pseudo_33)
41. Identify which PL rule is used in the following English argument: (David is a dad or Frank is a farmer) and Emma is an engineer. Therefore Emma is an engineer. (question id 05_pl_proofs_trans_11)
42. Identify which PL rule is used in the following English argument: Bob is not a builder. Chris is a carpenter. Therefore, Bob is not a builder and Chris is a carpenter. (question id 05_pl_proofs_trans_22)
43. Identify which PL rule is used in the following English argument: If Chris is not a carpenter and David is a dad, then Emma is not an engineer. Chris is not a carpenter and David is a dad. Therefore, Emma is not an engineer. (question id 05_pl_proofs_trans_57)
44. Identify which PL rule is used in the following English argument: Assume David is not a dad or Emma is an engineer (creating a subproof) and derive Frank is a farmer within that subproof. Finally, derive if (David is not a dad or Emma is an engineer}), then Frank is a farmer. (question id 05_pl_proofs_trans_86)
45. Identify which PL rule is used in the following English argument: Assume Bob is not a builder. Under that assumption, Chris is a carpenter and Chris is not a carpenter follows. Therefore, it is not the case that Bob is not a builder. (question id 05_pl_proofs_trans_96)
46. Identify which PL rule is used in the following English argument: Assume it is not the case that both (Al is beautiful and Bob is a builder). Under that assumption, Chris is a carpenter and not-Chris is a carpenter follows. Therefore, both Al is beautiful and Bob is a builder. (question id 05_pl_proofs_trans_112)
47. Identify which PL rule is used in the following English argument: Bob is not a builder. Therefore Bob is not a builder or Chris is a carpenter. (question id 05_pl_proofs_trans_125)
48. Identify which PL rule is used in the following English argument: Chris is a carpenter or David is a dad. First, assume Chris is a carpenter. Under this assumption Emma is not an engineer is the case. Second, assume David is not a dad. Under this assumption, Emma is not an engineer is also the case. Therefore, Emma is not an engineer is the case. (question id 05_pl_proofs_trans_144)
49. Identify which PL rule is used in the following English argument: Emma is an engineer if and only if (Frank is a farmer and Grace is a gardener), Frank is a farmer and Grace is a gardener. Therefore Emma is an engineer. (question id 05_pl_proofs_trans_170)