1. TF truth, falsity, and indeterminacy P is truth-functionally true iff it has the value T for any truth-value assignment. P is truth-functionally false iff it has the value F for any truth-value assignment. P is tf-false iff ~P is tf-true P is truth-functionally indeterminate iff it has the value T for some truth-value assignments, and the value F for some other truth-value assignments. P is tf-indeterminate iff it is neither tf-true nor th-false.

2. TF equivalence and consistency P and Q are truth-functionally equivalent iff P and Q do not have different truth-values for any truth-value assignment. A set of sentences is truth-functionally consistent iff there is a truth- value assignment that on which all the members of the set have the value T. A set of sentences is truth-functionally inconsistent iff it is not tf- consistent.

3. TF entailment and validity A set  of SL sentences truth-functionally entails a sentence P iff there is no truth-value assignment on which every member of  is true and P false.

4. TF entailment and validity A set  of SL sentences truth-functionally entails a sentence P iff there is no truth-value assignment on which every member of  is true and P false. An argument of SL is truth-functionally valid iff there is no truth- value assignment on which all the premises are true and the conclusion false.

5. TF entailment and validity A set  of SL sentences truth-functionally entails a sentence P iff there is no truth-value assignment on which every member of  is true and P false. An argument of SL is truth-functionally valid iff there is no truth- value assignment on which all the premises are true and the conclusion false. An argument of SL is truth-functionally invalid iff it is not tf-valid.

6. TF entailment and validity A set  of SL sentences truth-functionally entails a sentence P iff there is no truth-value assignment on which every member of  is true and P false. An argument of SL is truth-functionally valid iff there is no truth- value assignment on which all the premises are true and the conclusion false. An argument of SL is truth-functionally invalid iff it is not tf-valid. An argument is tf-valid iff the premises tf-entail the conclusion.

7. TF properties P is truth-functionally true iff it has the value T for any truth-value assignment. P is truth-functionally false iff ~P is tf-true. P is truth-functionally indeterminate iff P is neither tf-true nor tf-false. P and Q are truth-functionally equivalent iff P and Q do not have different truth- values for any truth-value assignment. A set of sentences is truth-functionally consistent iff there is a truth-value assignment that on which all the members of the set have the value T. A set  of SL sentences truth-functionally entails a sentence P iff there is no truth-value assignment on which every member of  is true and P false. An argument of SL is truth-functionally valid iff there is no truth-value assignment on which all the premises are true and the conclusion false.

8. 3.2E 1j ~B  ((B  D)  TT TF FT FF

9. 3.2E 1j ~B  ((B  D)  FTT FTF TFT TFF

10. 3.2E 1j ~B  ((B  D)  FTTT FTTF TFT TFF

11. 3.2E 1j ~B  ((B  D)  FTTT FTTF TFT TFFT

12. 3.2E 1j ~B  ((B  D)  FTTT FTTF TFTTT TFFT

13. 3.2E 1j ~B  ((B  D)  FTTT FTTF TFTTTT TFTFT

14. 3.2E 1j ~B  ((B  D)  FT T T FT T F TF T TTT TF T FT

15. 3.2E 1l (M  ~N)&(M  N) TT TF FT FF

16. 3.2E 1l (M  ~N)&(M  N) T F T T T F F F T F T F

17. 3.2E 1l (M  ~N)&(M  N) T FF T T TT F F TF T F FT F

18. 3.2E 1l (M  ~N)&(M  N) T FF T T T TT F F F TF T F F FT F T

19. 3.2E 1l (M  ~N)&(M  N) T FF T T T TT F F F TF T F F FT F T

20. 3.2E 1l (M  ~N)&(M  N) T FF T F T T TT F F F F TF T F F F FT F F T

21. 3.3E 1d (C&(B  A))  ((C&B)  A) TTT TTF TFT TFF FTT FTF FFT FFF

22. 3.3E 1d (C&(B  A))  ((C&B)  A) TTT TTF TFT TFF FFTT FFTF FFFT FFFF

23. 3.3E 1d (C&(B  A))  ((C&B)  A) TTT TTF TFT TFFF FFTT FFTF FFFT FFFF

24. 3.3E 1d (C&(B  A))  ((C&B)  A) TTTT TTTF TFTT TFFF FFTT FFTF FFFT FFFF

25. 3.3E 1d (C&(B  A))  ((C&B)  A) TTTTT TTTTF TTFTT TFFFF FFTT FFTF FFFT FFFF

26. 3.3E 1d (C&(B  A))  ((C&B)  A) TTTTTT TTTTF TTFTTT TFFFF FFTTT FFTF FFFTT FFFF

27. 3.3E 1d (C&(B  A))  ((C&B)  A) TTTTTT TTTTFT TTFTTT TFFFFF FFTTT FFTFF FFFTT FFFFF

28. 3.3E 1d (C&(B  A))  ((C&B)  A) TTTTTT TTTTFTT TTFTTT TFFFFFF FFTTT FFTFFF FFFTT FFFFFF

29. 3.3E 1d (C&(B  A))  ((C&B)  A) TTTTTT TTTTFTT TTFTTT TFFFFFF FFTTT FFTFFF FFFTT FFFFFF

30. 3.3E 1d (C&(B  A))  ((C&B)  A) TTTTTT TTTTFTT TTFTTT TFFFFFF FFTT F T FFTFFF FFFTT FFFFFF

31. 3.4E 1f U  (W&H)W  (U  H)H  ~H 1TTT 2TTF 3TFT 4TFF 5FTT 6FTF 7FFT 8FFF

32. 3.4E 1f U  (W&H)W  (U  H)H  ~H 1T T TT T 2T T TF T 3T T FT F 4T T FF F 5F T TT T 6F F TF F 7F F FT F 8F F FF T

33. 3.4E 1f U  (W&H)W  (U  H)H  ~H 1T T TT T T 2T T TF T T 3T T FT F T 4T T FF F T 5F T TT T T 6F F TF F T 7F F FT F T 8F F FF T T

34. 3.5E1b B  (A  ~C)(C  A)  B~B  A~(A  C) 1 TTT 2 TTF 3 FTT 4 FTF 5 TFT 6 TFF 7 FFT 8 FFF

35. 3.5E1b B  (A  ~C)(C  A)  B~B  A~(A  C) 1TTFTF 2TTTFF 3FTFTT 4FTTFT 5TFFTF 6TFTFF 7FFFTT 8FFTFT

36. 3.5E1b B  (A  ~C)(C  A)  B~B  A~(A  C) 1TTTFTF 2TTTTFF 3FTFTT 4FTTFT 5TTFFTF 6TTFTFF 7FFFTT 8FFTFT

37. 3.5E1b B  (A  ~C)(C  A)  B~B  A~(A  C) 1TTTFTF 2TTTTFF 3FTFFTT 4FTTTFT 5TTFFTF 6TTFTFF 7FFFFTT 8FFFTFT

38. 3.5E1b B  (A  ~C)(C  A)  B~B  A~(A  C) 1TTTFTF 2TTTTFF 3FFTFFTT 4FTTTTFT 5TTFFTF 6TTFTFF 7FFFFFTT 8FFFFTFT

39. 3.5E1b B  (A  ~C)(C  A)  B~B  A~(A  C) 1TTTFTF 2TTTTFTF 3FFTFFTT 4FTTTTFTT 5TTFFTF 6TTFTFTF 7FFFFFTT 8FFFFTFTT

40. 3.5E1b B  (A  ~C)(C  A)  B~B  A~(A  C) 1TTTFTTF 2TTTTFTF 3FFTFFTTT 4FTTTTFTT 5TTFFTF 6TTFTFTF 7FFFFFTT 8FFFFTFTT

41. 3.5E1b B  (A  ~C)(C  A)  B~B  A~(A  C) 1TTTFTTF 2TTTTFTF 3FFTFFTTT 4FTTTTFTT 5TTFFTFF 6TTFTFTF 7FFFFFTFT 8FFFFTFTT

42. 3.5E1b B  (A  ~C)(C  A)  B~B  A~(A  C) 1TTTFTTTF 2TTTTFTTF 3FFTFFTTFT 4FTTTTFTFT 5TTFFTFFF 6TTFTFTTF 7FFFFFTFTT 8FFFFTFTFT

43. 3.5E1b B  (A  ~C)(C  A)  B~B  A~(A  C) 1TTTFTTTFT 2TTTTFTTFT 3FFTFFTTFTT 4FTTTTFTFTT 5TTFFTFFF 6TTFTFTTF 7FFFFFTFTTT 8FFFFTFTFTT

44. 3.5E1b B  (A  ~C)(C  A)  B~B  A~(A  C) 1TTTFTTTFT 2TTTTFTTFT 3FFTFFTTFTT 4FTTTTFTFTT 5TTFFTFFFF 6TTFTFTTFF 7FFFFFTFTTT 8FFFFTFTFTT

45. 3.5E1b B  (A  ~C)(C  A)  B~B  A~(A  C) 1TTTFTTTFTT 2TTTTFTTFTT 3FFTFFTTFTTT 4FTTTTFTFTTT 5TTFFTFFFFT 6TTFTFTTFF 7FFFFFTFTTTT 8FFFFTFTFTT

46. 3.5E1b B  (A  ~C)(C  A)  B~B  A~(A  C) 1TTTFTTTFTT 2TTTTFTTFTT 3FFTFFTTFTTT 4FTTTTFTFTTT 5TTFFTFFFFT 6TTFTFTTFFF 7FFFFFTFTTTT 8FFFFTFTFTTF

47. 3.5E1b B  (A  ~C)(C  A)  B~B  A~(A  C) 1TTTFTTTFTFT 2TTTTFTTFTFT 3FFTFFTTFTTFT 4FTTTTFTFTTFT 5TTFFTFFFFFT 6TTFTFTTFFTF 7FFFFFTFTTTFT 8FFFFTFTFTTTF

48. 3.5E1b B  (A  ~C)(C  A)  B~B  A~(A  C) 1TTTFTTTFTFT 2TTTTFTTFTFT 3FFTFFTTFTTFT 4FTTTTFTFTTFT 5TTFFTFFFFFT 6TTFTFTTFFTF 7FFFFFTFTTTFT 8FFFFTFTFTTTF

49. 3.5E 1D ~(Y  A)~Y~AW&~W 1FTTTFFTFF 2FTTTFFFFT 3TTFFFTTFF 4TTFFFTFFT 5TFFTTFTFF 6TFFTTFFFT 7FFTFTTTFF 8FFTFTTFFT

50. shortened truth tables Show that ~B  (B&~B) is not tf-true

51. shortened truth tables Show that ~B  (B&~B) is not tf-true B~B  (B&~B) F

52. shortened truth tables Show that ~B  (B&~B) is not tf-true B~B  (B&~B) FFF

53. shortened truth tables Show that ~B  (B&~B) is not tf-true B~B  (B&~B) FTFF

54. shortened truth tables Show that ~B  (B&~B) is not tf-true B~B  (B&~B) TFTFTFT

55. shortened truth tables Show that ~B  (B&~B) is not tf-true B~B  (B&~B) TFTFTFFT

56. shortened truth tables Show that (~B  ~A)&C is not tf-false AB(~B  ~A)&B

57. shortened truth tables Show that (~B  ~A)&C is not tf-false AB(~B  ~A)&B T

58. shortened truth tables Show that (~B  ~A)&C is not tf-false AB(~B  ~A)&B TTT

59. shortened truth tables Show that (~B  ~A)&C is not tf-false AB(~B  ~A)&B TTTT

60. shortened truth tables Show that (~B  ~A)&C is not tf-false AB(~B  ~A)&B TTTTT

61. shortened truth tables Show that (~B  ~A)&C is not tf-false AB(~B  ~A)&B TFTTTT

62. shortened truth tables Show that (~B  ~A)&C is not tf-false AB(~B  ~A)&B TFTTTTT

63. shortened truth tables Show that (~B  ~A)&C is not tf-false AB(~B  ~A)&B FTFTTTFTT

64. shortened truth tables Show that (A  B)  (B  A) is not tf-false AB(A  B)  (B  A) T

65. shortened truth tables Show that (A  B)  (B  A) is not tf-false AB(A  B)  (B  A) TTT FTF

66. shortened truth tables Show that (A  B)  (B  A) is not tf-false AB(A  B)  (B  A) TTT TFFTTFF

67. shortened truth tables Show that (A  B)  (B  A) is not tf-false AB(A  B)  (B  A) TTT ?? T F F T T F F COTRADICTION!

68. shortened truth tables Show that (A  B)  (B  A) is not tf-false AB(A  B)  (B  A) TTT

69. shortened truth tables Show that (A  B)  (B  A) is not tf-false AB(A  B)  (B  A) TTTTT FTTTT FTFTT

70. shortened truth tables Show that (A  B)  (B  A) is not tf-false AB(A  B)  (B  A) TTTTT FTFTTTTTF FTFTT

71. shortened truth tables Show that (A  B)  (B  A) is not tf-false AB(A  B)  (B  A) TTTTT FTFTTT TTF FTFTT CONTRADICTION!

72. shortened truth tables Show that (A  B)  (B  A) is not tf-false AB(A  B)  (B  A) TTTTT FTFTT

73. shortened truth tables Show that (A  B)  (B  A) is not tf-false AB(A  B)  (B  A) TTTTTTTTT FTFTT

74. shortened truth tables Show that (A  B)  (B  A) is not tf-false AB(A  B)  (B  A) TTTTTTTTT

75. shortened truth tables Show that (A  B)  (B  A) is not tf-true AB(A  B)  (B  A) F

76. shortened truth tables Show that (A  B)  (B  A) is not tf-true AB(A  B)  (B  A) FFF

77. shortened truth tables Show that (A  B)  (B  A) is not tf-true AB(A  B)  (B  A) TFFFTFF

78. shortened truth tables Show that (A  B)  (B  A) is not tf-true AB(A  B)  (B  A) ??TFFFTFF CONTRADICTION! Therefore, the sentence is tf-true

79. shortened truth tables Practice Show that: {A  (B&C), B  (A  C), C  ~C} is tf-consistent {B  (A&~C), (C  A)  B, ~B  A}  ~(A  C)

80. shortened truth tables Practice Show that: {A  (B&C), B  (A  C), C  ~C} is tf-consistent {B  (A&~C), (C  A)  B, ~B  A}  ~(A  C) ABC A  (B&C)B  (A  C)C  ~C TTT

81. shortened truth tables Practice Show that: {A  (B&C), B  (A  C), C  ~C} is tf-consistent {B  (A&~C), (C  A)  B, ~B  A}  ~(A  C) ABC A  (B&C)B  (A  C)C  ~C T T T TT

82. shortened truth tables Practice Show that: {A  (B&C), B  (A  C), C  ~C} is tf-consistent {B  (A&~C), (C  A)  B, ~B  A}  ~(A  C) ABC A  (B&C)B  (A  C)C  ~C TTT T T TTT TT

83. shortened truth tables Practice Show that: {A  (B&C), B  (A  C), C  ~C} is tf-consistent {B  (A&~C), (C  A)  B, ~B  A}  ~(A  C) ABC A  (B&C)B  (A  C)C  ~C TTT T T TTTT T TTT T T

84. shortened truth tables Practice Show that: {A  (B&C), B  (A  C), C  ~C} is tf-consistent {B  (A&~C), (C  A)  B, ~B  A}  ~(A  C) ABC A  (B&C)B  (A  C)C  ~C TTT T T TTTT T TTTT T FT

85. shortened truth tables Practice Show that: {A  (B&C), B  (A  C), C  ~C} is tf-consistent {B  (A&~C), (C  A)  B, ~B  A}  ~(A  C) ABC A  (B&C)B  (A  C)C  ~C TTT T T TTTT T TTTT T FT B  (A&~C)(C  A)  B~B  A~(A  C) TTTF

86. shortened truth tables Practice Show that: {A  (B&C), B  (A  C), C  ~C} is tf-consistent {B  (A&~C), (C  A)  B, ~B  A}  ~(A  C) ABC A  (B&C)B  (A  C)C  ~C TTT T T TTTT T TTTT T FT B  (A&~C)(C  A)  B~B  A~(A  C) TTTFT

87. shortened truth tables Practice Show that: {A  (B&C), B  (A  C), C  ~C} is tf-consistent {B  (A&~C), (C  A)  B, ~B  A}  ~(A  C) ABC A  (B&C)B  (A  C)C  ~C TTT T T TTTT T TTTT T FT B  (A&~C)(C  A)  B~B  A~(A  C) TTTTTFT

88. shortened truth tables Practice Show that: {A  (B&C), B  (A  C), C  ~C} is tf-consistent {B  (A&~C), (C  A)  B, ~B  A}  ~(A  C) ABC A  (B&C)B  (A  C)C  ~C TTT T T TTTT T TTTT T FT B  (A&~C)(C  A)  B~B  A~(A  C) TTTTTTTFT

89. shortened truth tables Practice Show that: {A  (B&C), B  (A  C), C  ~C} is tf-consistent {B  (A&~C), (C  A)  B, ~B  A}  ~(A  C) ABC A  (B&C)B  (A  C)C  ~C TTT T T TTTT T TTTT T FT B  (A&~C)(C  A)  B~B  A~(A  C) TTTTTFTTFT

90. shortened truth tables Practice Show that: {A  (B&C), B  (A  C), C  ~C} is tf-consistent {B  (A&~C), (C  A)  B, ~B  A}  ~(A  C) ABC A  (B&C)B  (A  C)C  ~C TTT T T TTTT T TTTT T FT B  (A&~C)(C  A)  B~B  A~(A  C) TTTTTFFTTTTTTFTTF

91. shortened truth tables Practice Show that: {A  (B&C), B  (A  C), C  ~C} is tf-consistent {B  (A&~C), (C  A)  B, ~B  A}  ~(A  C) ABC A  (B&C)B  (A  C)C  ~C TTT T T TTTT T TTTT T FT B  (A&~C)(C  A)  B~B  A~(A  C) TTTTTFFTTTTFTTTFTTF