TF truth, falsity, and indeterminacy

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

9. 3.2E 1j

10. 3.2E 1j

11. 3.2E 1j

12. 3.2E 1j

13. 3.2E 1j

14. 3.2E 1j

15. 3.2E 1l

16. 3.2E 1l

17. 3.2E 1l

18. 3.2E 1l

19. 3.2E 1l

20. 3.2E 1l

21. 3.3E 1d

22. 3.3E 1d

23. 3.3E 1d

24. 3.3E 1d

25. 3.3E 1d

26. 3.3E 1d

27. 3.3E 1d

28. 3.3E 1d

29. 3.3E 1d

30. 3.3E 1d

31. 3.4E 1f

32. 3.4E 1f

33. 3.4E 1f

34. 3.5E1b

35. 3.5E1b

36. 3.5E1b

37. 3.5E1b

38. 3.5E1b

39. 3.5E1b

40. 3.5E1b

41. 3.5E1b

42. 3.5E1b

43. 3.5E1b

44. 3.5E1b

45. 3.5E1b

46. 3.5E1b

47. 3.5E1b

48. 3.5E1b

49. 3.5E 1D