#6 final
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School
East Los Angeles College *
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Course
101
Subject
Philosophy
Date
Dec 6, 2023
Type
docx
Pages
5
Uploaded by ChefDangerBear36
Question 1
10 / 10 pts
Use the older, Aristotelian system to determine if the following categorical
syllogism is valid or invalid. Valid = If the premises are true, the conclusion
must be true. Draw for yourself a Venn Diagram and read it correctly, then
report your final answer: VALID or INVALID.
(1) No M is P.
All M are S.
Therefore, some S are not P.
Your Answer:
VALID
Question 2
10 / 10 pts
Use the older, Aristotelian system to determine if the following categorical
syllogism is valid or invalid. Valid = If the premises are true, the conclusion
must be true. Draw for yourself a Venn Diagram and read it correctly, then
report your final answer: VALID or INVALID.
(2) All M are P.
Some M are not S.
Therefore, some S are P.
Your Answer:
INVALID
Question 3
10 / 10 pts
Determine if the following sentence in propositional logic is TRUE or FALSE
(the value you end up with under the main operator), assuming A is true, B is
true, and C is false. The truth table definitions are given at the bottom of the
Deduction Rules sheet, located in the Modules in Canvas. Write your final
answer: TRUE or FALSE:
(3) -[A --> (C v B)]
Your Answer:
FALSE
Question 4
10 / 10 pts
Determine if the following sentence in propositional logic is a
CONTRADICTION (all false under the main operator), a TAUTOLOGY (all true
under the main operator), or CONTINGENT (a mix of true and false under the
main operator). The truth table definitions are given at the bottom of the
Deduction Rules sheet, located in the Modules in Canvas. Report your final
answer as: CONTRADICTION, TAUTOLOGY, or CONTINGENT.
(4) -B --> -(A & B)
Your Answer:
TAUTOLOGY
Question 5
10 / 10 pts
Determine if the following argument (two premises and a conclusion) is
VALID or INVALID in propositional logic. Build a truth table for yourself and
then read it accurately. Invalid = T T F on a single row across, the two
premises are true under their main operators at the same time the
conclusion is false under its main operator. Report your final answer as:
VALID or INVALID:
(5) -(N <--> P) N therefore -P
Your Answer:
VALID
Question 6
5 / 10 pts
Determine if the following argument (two premises and a conclusion) is
VALID or INVALID in propositional logic. Build a truth table for yourself and
then read it accurately. Invalid = T T F: on a single row across, the two
premises are true under their main operators at the same time the
conclusion is false under its main operator Report your final answer as: VALID
or INVALID.
(6) P --> (-Q v R) P & -R therefore -Q
Your Answer:
INVALID
-
valid
Question 7
10 / 10 pts
Annotate the following natural deduction. Accurately state where each line of
the deduction came from, using which of the valid 17 rules. Use your
Deduction Rules Sheet, located in the Modules in Canvas.
# your answers 5, 6, 7, 8, 9, 10, and 11.
(7)
1.
(P & Q) v (R & S)
2.
-H --> -Z
3.
S --> (W & Z)
4.
-P
/ H
5.
-P v -Q ___
6.
-(P & Q) ___
7.
R & S ___
8.
S ___
9.
W & Z ___
10.
Z ___
11.
H ___
Your Answer:
5. 4 ADD
6. 5 DM
7. 1,6 DS
8. 7 SIMP
9. 3,8 MP
10. 9 SIMP
11. 2,10 MT
Question 8
10 / 10 pts
Annotate the following natural deduction. Accurately state where each line of
the deduction came from, using which of the valid 17 rules. Use your
Deduction Rules Sheet, located in the Modules in Canvas.
# your answers 4, 5, 6, and 7.
(8)
1.
-(P & Q) --> (R v S)
2.
-P v -Q
3.
T
/ (T & R) v (T & S)
4.
-(P & Q) ___
5.
R v S ___
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6.
T & (R v S) ___
7.
(T & R) v (T & S) ___
Your Answer:
4. 2 DM
5. 1,4 MP
6. 3,5 CONJ
7 . 6 DIST
Question 9
10 / 10 pts
Annotate the following natural deduction. Accurately state where each line of
the deduction came from, using which of the valid 17 rules. Use your
Deduction Rules Sheet, located in the Modules in Canvas.
# your answers 6, 7, 8, 9, 10, 11, 12, and 13.
(9)
1.
-F --> W
2.
-D v -D
3.
H v G
4.
(F v G) --> D
5.
H --> -Z
/ W v -Z
6.
-D ___
7.
-(F v G) ___
8.
-F & -G ___
9.
-G ___
10.
H ___
11.
H v -F ___
12.
-F v H ___
13.
W v -Z ___
Your Answer:
6. 2 TAUT
7. 4,6 MT
8. 7 DM
9. 8 SIMP
10. 3,9 DS
11. 10 ADD
12. 11 COM
13. 1,5,12 CD
Question 10
10 / 10 pts
Annotate the following natural deduction. Accurately state where each line of
the deduction came from, using which of the valid 17 rules. Use your
Deduction Rules Sheet, located in the Modules in Canvas.
# your answers 4, 5, 6, 7, and 8.
(10)
1.
-Z v A
2.
C v Z
3.
C --> B
/ -A --> B
4.
Z --> A ___
5.
-C --> Z ___
6.
-C --> A ___
7.
-A --> C ___
8.
-A --> B ___
Your Answer:
4. 1 IMPL
5. 2 IMPL
6. 4,5 HS
7. 6 TRANS
8. 3,7 HS