Notes on computational linguistics.pdf - UCLA Department of ...

Stabler - Lx 185/209 2003
39. (A ↔ B) → ((C ↔ A) ↔ (C ↔ B))
40. (A ∨ (B ∨ C) ↔ (B ∨ (A ∨ C))
41. (A ∨ (B ∨ C)) → ((A ∨ B) ∨ C) (Associative Law for Disjunction)
42. ¬(A ∧ B) ↔ (¬A ∨¬B) (De Morgan’s Law)
43. ¬(A ∨ B) ↔ (¬A ∧¬B) (De Morgan’s Law)
44. (A ∧ B) ↔ ¬(¬A∨¬B) (De Morgan’s Law)
45. (A ∨ B) ↔ ¬(¬A∧¬B) (De Morgan’s Law)
46. (A ∧ B) ↔ (B ∧ A) (Commutative Law for Conjunction)
47. (A ∧ B) → A (Law of Simplification)
48. (A ∧ B) → B (Law of Simplification)
49. (A ∧ A) → A (Law of Tautology for Conjunction)
50. (A ∧ (B ∧ C)) ↔ ((A ∧ B) ∧ C) (Associative Law for Conjunction)
51. (A → (B → C)) ↔ ((A ∧ B) → C) (Export-Import Law)
52. (A → B) ↔ ¬(A ∧¬B)
53. (A → B) ↔ (¬A ∨ B) ES says: know this one!
54. (A ∨ (B ∧ C)) ↔ ((A ∨ B) ∧ (A ∨ C)) (Distributive Law)
55. (A ∧ (B ∨ C)) ↔ ((A ∧ B) ∨ (A ∧ C)) (Distributive Law)
56. ((A ∧ B) ∨ (C ∧ D)) ↔ (((A ∨ C) ∧ (A ∨ D)) ∧ (B ∨ C) ∧ (B ∨ D))
57. A → ((A ∧ B) ↔ B)
58. A → ((B ∧ A) ↔ B)
59. A → ((A → B) ↔ B)
60. A → ((A ↔ B) ↔ B)
61. A → ((B ↔ A) ↔ B)
62. ¬A → ((A ∨ B) ↔ B)
63. ¬A → ((B ∨ A) ↔ B)
64. ¬A → (¬(A ↔ B) ↔ B)
65. ¬A → (¬(B ↔ A) ↔ B)
66. A ∨¬A (Law of Excluded Middle)
67. ¬(A ∧¬A) (Law of Contradiction)
68. (A ↔ B) ↔ ((A ∧ B) ∨ (¬A ∧¬B))
69. ¬(A ↔ B) ↔ (A ↔ ¬B)
70. ((A ↔ B) ∧ (B ↔ C)) → (A ↔ C)
71. ((A ↔ B) ↔ A) ↔ B
72. (A ↔ (B ↔ C)) ↔ ((A ↔ B) ↔ C)
73. (A → B) ↔ (A → (A ∧ B))
74. (A → B) ↔ (A ↔ (A ∧ B))
75. (A → B) ↔ ((A ∨ B) → B)
76. (A → B) ↔ ((A ∨ B) ↔ B)
77. (A → B) ↔ (A → (A → B))
78. (A → (B ∧ C)) ↔ ((A → B) ∧ (A → C))
79.
80.
((A ∨ B) → C) ↔ ((A → C) ∧ (B → C))
(A → (B ∨ C)) ↔ ((A → B) ∨ (A → C))
77