Exercise on page 48
- Modal relations between proposition-sets:
- is inconsistent with v.
- is inconsistent with none (i.e. is inconsistent with none of i-v).
- is inconsistent with i, ii, iii, iv, v.
- is inconsistent with none.
- is inconsistent with none.
- is consistent with i, ii, iii, iv.
- is consistent with i, ii, iii, iv, v.
- is consistent with none.
- is consistent with i, ii, iii, iv, v.
- is consistent with i, ii, iii, iv, v.
- implies i.
- implies none.
- implies i, ii, iii, iv, v.
- implies none.
- implies iv.
- is equivalent to none.
- is equivalent to none.
- is equivalent to none.
- is equivalent to none.
- is equivalent to iv.
- iii.
- {Sylvia is Diane's mother, Sylvia is female and is a parent of Diane's,
Diane is a child of Sylvia who is female.}
- {Two plus two equals four, It is raining or it is not raining, Whatever
is blue is colored}
Exercise on pages 55-57
Part A
1. | P | | 1, 2, 5 |
2. | Q | | 1, 3, 6 |
3. | P | | 6, 7, 9, 10, 11, 12, 13, 14, 15 |
4. | Q | | 5, 8, 9, 10, 11, 12, 13, 14, 15 |
5. | P is actually true | | 1, 2, 5 |
6. | P Q | | 1, 3, 4, 6, 8, 9, 11 |
7. | Q P | | 1, 2, 4, 5, 7, 9, 13 |
8. | P O Q | | 1, 5, 6, 9, 11, 13, 14, 15 |
9. | P Ø Q | | 2, 3, 4, 7, 8, 10, 12 |
10. | Contradictories | | 2, 3, 10 |
11. | Contraries | | 4, 7, 8, 12 |
12. | Subcontraries | | 1, 5, 6, 14 |
13. | P Q | | 1, 4, 9 |
14. | P and Q | | 1, 5, 6, 9, 10, 11, 12, 13, 14, 15 |
15. | P, Q, and P Ø Q | | 10, 12 |
16. | ~(P Q) and ~(Q P) | | 10, 12, 14, 15 |
17. | (P Q) and (P O Q) | | 1, 6, 9, 11 |
18. | (P Q) and (P Ø Q) | | 3, 4, 8 |
19. | (P Q) and ~(Q P) | | 3, 6, 8, 11 |
20. | (P O Q) and ~(P Q) | | 5, 13, 14, 15 |
21. | (P Ø Q) and ~(P Q) | | 2, 7, 10, 12 |
22. | P P | | 1 - 15 (i.e. every case) |
23. | P, Q, and (P Q) | | 6 |
24. | P, Q, and (P Q) | | none (this is impossible) |
25. | (P Q) and (P Ø Q) | | 4 |
26. | P ~P | | 3, 4, 8 |
27. | ~P P | | 1, 2, 5 |
28. | P O ~P | | none (an impossible case) |
29. | (P ~Q) and (P O Q) | | none (an impossible case) |
30. | P and ~P | | none (an impossible case) |
31. | | WD1 | | P: All squares have four sides.
Q: Whatever is green, is red or green. |
32. | | WD2 | | P: 2 + 2 = 4
Q: 5 x 7 = 57 |
33. | | WD3 | | P: Some triangles have five sides.
Q: All aunts are females. |
34. | | WD4 | | P: It is raining and it is not raining.
Q: The Prime Minister of Canada knows that 2 + 2 = 7. |
35. | | WD5 | | P: If anyone knows that it is raining, then it is raining.
Q: It is raining. |
36. | | WD6 | | P: Two liters of water mixed with two liters of alcohol yields
four liters of liquid.
Q: 2 + 2 = 4 |
37. | | WD7 | | P: Today is Tuesday.
Q: Today is Tuesday and the day before Saturday. |
38. | | WD8 | | P: There are exactly five women here and the women outnumber the men
(exactly) by a factor of two.
Q: Someone knows all the words to the national anthem. |
39. | | WD9 | | P: John is the same age as Judy.
Q: Judy is the same age as John. |
40. | | WD10 | | P: Canada is a member of the British Commonwealth.
Q: It is false that Canada is a member of the British Commonwealth. |
41. | | WD11 | | P: Judy loves strawberry ice cream.
Q: Judy loves at least one flavor of ice cream. |
42. | | WD12 | | P: Aziz is exactly 15 years old.
Q: Aziz is exactly 19 years old. |
42. | | WD13 | | P: Judy loves at least one flavor of ice cream.
Q: Judy loves strawberry ice cream. |
44. | | WD14 | | P: It is false that Aziz is exactly 15 years old.
Q: It is false that Aziz is exactly 19 years old. |
45. | | WD15 | | P: He is stubborn.
Q: You are dogmatic. |
Part B
46. | ~(P Q) | | 2, 5, 7, 10, 12, 13, 14, 15 |
47. | (~P Q) | | 1, 2, 3, 5, 6, 10, 14 |
48. | (P Q) and (~P Q) | | 1, 3, 6 |
Part C
49. | | How many ... ? | | 32 |
50. | | (P Q) and ~Q | | 4 [ = 4a], 8b, 9b, 11c |
51. | | Worlds-diagram 11 with an "X" in the leftmost segment,
i.e. Worlds-diagram 11a. |
52. | | yes |
53. | | no |
54. | | no |
55. | | Worlds-diagram 11 with an "X" in the rightmost segment,
i.e. Worlds-diagram 11c. |
|