| Phil. 1: Introduction to Logic | |
| Schedule | |
| Answer Key | |
Exercise 4.5
Part I
1. (a) false, (b) true, (c) false.
2. (a) undetermined, (b) undetermined, (c) true.
3. (a) false, (b) false, (c) true.
4. (a) undetermined, (b) true, (c) undetermined.
5. (a) undetermined, (b) false, (c) undetermined.
6. (a) false, (b) true, (c) true.
7. (a) false, (b) undetermined, (c) undetermined.
8. (a) true, (b) false, (c) true.
Part II
1. Valid.
2. Invalid (illicit subalternation).
3. Valid.
4. Invalid (illicit subcontrary).
5. Valid.
6. Valid.
7. Invalid (illicit contrary).
8. Invalid (illicit subcontrary).
9. Invalid (illicit contrary).
10. Valid.
Part III
1. All non-B are A. (True)
2. All A are non-B. (False)
3. All A are B. (True)
4. Some non-A are B. (Undetermined)
5. Some A are non-B. (True)
6. No non-B are non-A. (Undetermined)
7. No non-A are B. (False)
8. Some A are B. (False)
9. No non-B are A. (False)
10. Some non-A are not non-B. (True)
11. Contradictory (False)
12. Conversion (True)
13. Obversion (False)
14. Subalternation (Undetermined)
15. Conversion (Undetermined)
16. Contradictory (True)
17. Contraposition (True)
18. Subalternation (True)
19. Contrary Undetermined)
20. Subcontrary (True)
Part IV
1. All I are C.
Some I are C. (Subalt.)
Some C are I. (Conv.)
2. No non-G are E.
Some non-G are not E. (Subalt.)
Some non-E are not G. (Contrap.)
3. F: Some F are non-T.
F: Some F are not T. (Obv.)
All F are T. (Contradic.)
4. All E are A.
F: No E are A. (Contrary)
F: No A are E. (Conv.)
F: All A are non-E. (Obv.)
5. No non-P are F.
No F are non-P. (Conv.)
All F are P. (Obv.)
F: Some F are not P. (Contradic.)
6. F: Some G are non-B.
F: Some G are not B. (Obv.)
Some G are B. (Subcon.)
Some B are G. (Conv.)
7. Some P are not non-S.
Some P are S. (Obv.)
Some S are P. (Conv.)
F: No S are P. (Contradic.)
8. F: No non-H are F.
F: No F are non-H. (Conv.)
F: All F are H. (Obv.)
Some F are not H. (Contradic.)
9. F: Some non-L are not S.
Some non-L are S. (Subcon.)
Some S are non-L. (Conv.)
Some S are not L. (Obv.)
10. F: Some F are not A.
F: No F are A. (Subalt.)
F: No A are F. (Conv.)
F: All A are non-F. (Obv.)
Part V
1. All J are A.
J A
F: No J are A.
Valid.
J A
2. F: No P are F.
P F
All P are F.
Invalid.
P F
3. F: Some P are A.
P A
Some P are not A.
Invalid.
Exist. fal. P A
4. No P are A.
P A
All P are non-A.
Valid.
P A
5. F: Some M are P.
M P
F: All M are P.
Valid.
M P
6. Some E are F.
E F
Some F are not E.
Invalid.
E F
7. Some S are H.
S H
F: All H are non-S.
Valid.
S H
8. All T are O.
T O
F: All T are non-O.
Invalid.
Exist. fal. T O
9. F: Some C are not non-A.
C A
Some A are non-C.
Valid.
C A
10. No S are non-O.
S O
All O are S.
Invalid.
S O
11. F: Some M are P.
M P
Some non-P are M
Invalid. Exist. fal.
M P
12. All S are D.
S D
F: Some non-D are S.
Valid.
S D
13. Some T are non-I.
T I
Some non-T are I.
Invalid.
T I
14. F: Some N are non-O.
N O
F: No O are N.
Invalid.
Exist. fal. N O
15. All B are T.
B T
Some B are not non-T.
Valid.
B T
Exercise 4.5
Part I
1. (a) false, (b) true, (c) false.
2. (a) undetermined, (b) undetermined, (c) true.
3. (a) false, (b) false, (c) true.
4. (a) undetermined, (b) true, (c) undetermined.
5. (a) undetermined, (b) false, (c) undetermined.
6. (a) false, (b) true, (c) true.
7. (a) false, (b) undetermined, (c) undetermined.
8. (a) true, (b) false, (c) true.
Part II
1. Valid.
2. Invalid (illicit subalternation).
3. Valid.
4. Invalid (illicit subcontrary).
5. Valid.
6. Valid.
7. Invalid (illicit contrary).
8. Invalid (illicit subcontrary).
9. Invalid (illicit contrary).
10. Valid.
Part III
1. All non-B are A. (True)
2. All A are non-B. (False)
3. All A are B. (True)
4. Some non-A are B. (Undetermined)
5. Some A are non-B. (True)
6. No non-B are non-A. (Undetermined)
7. No non-A are B. (False)
8. Some A are B. (False)
9. No non-B are A. (False)
10. Some non-A are not non-B. (True)
11. Contradictory (False)
12. Conversion (True)
13. Obversion (False)
14. Subalternation (Undetermined)
15. Conversion (Undetermined)
16. Contradictory (True)
17. Contraposition (True)
18. Subalternation (True)
19. Contrary Undetermined)
20. Subcontrary (True)
Part IV
1. All I are C.
Some I are C. (Subalt.)
Some C are I. (Conv.)
2. No non-G are E.
Some non-G are not E. (Subalt.)
Some non-E are not G. (Contrap.)
3. F: Some F are non-T.
F: Some F are not T. (Obv.)
All F are T. (Contradic.)
4. All E are A.
F: No E are A. (Contrary)
F: No A are E. (Conv.)
F: All A are non-E. (Obv.)
5. No non-P are F.
No F are non-P. (Conv.)
All F are P. (Obv.)
F: Some F are not P. (Contradic.)
6. F: Some G are non-B.
F: Some G are not B. (Obv.)
Some G are B. (Subcon.)
Some B are G. (Conv.)
7. Some P are not non-S.
Some P are S. (Obv.)
Some S are P. (Conv.)
F: No S are P. (Contradic.)
8. F: No non-H are F.
F: No F are non-H. (Conv.)
F: All F are H. (Obv.)
Some F are not H. (Contradic.)
9. F: Some non-L are not S.
Some non-L are S. (Subcon.)
Some S are non-L. (Conv.)
Some S are not L. (Obv.)
10. F: Some F are not A.
F: No F are A. (Subalt.)
F: No A are F. (Conv.)
F: All A are non-F. (Obv.)
Part V
1. All J are A.
J A
F: No J are A.
Valid.
J A
2. F: No P are F.
P F
All P are F.
Invalid.
P F
3. F: Some P are A.
P A
Some P are not A.
Invalid.
Exist. fal. P A
4. No P are A.
P A
All P are non-A.
Valid.
P A
5. F: Some M are P.
M P
F: All M are P.
Valid.
M P
6. Some E are F.
E F
Some F are not E.
Invalid.
E F
7. Some S are H.
S H
F: All H are non-S.
Valid.
S H
8. All T are O.
T O
F: All T are non-O.
Invalid.
Exist. fal. T O
9. F: Some C are not non-A.
C A
Some A are non-C.
Valid.
C A
10. No S are non-O.
S O
All O are S.
Invalid.
S O
11. F: Some M are P.
M P
Some non-P are M
Invalid. Exist. fal.
M P
12. All S are D.
S D
F: Some non-D are S.
Valid.
S D
13. Some T are non-I.
T I
Some non-T are I.
Invalid.
T I
14. F: Some N are non-O.
N O
F: No O are N.
Invalid.
Exist. fal. N O
15. All B are T.
B T
Some B are not non-T.
Valid.
B T