-
-
Assignment 5
This assignment should take you approximately five hours to complete. It consists of fifteen questions. The value of each question is indicated by the question. Be concise and approach each question directly. If the question asks for an explanation with your answer, then the quality of that explanation counts in your mark for the question. The total possible high mark for this assignment is 100 marks.
Translation Questions 1 - 10: (5 marks each 50 marks total) Translate the following ordinary language statements into predicate logic symbolic form. You can use the predicate letters that are provided. Questions #7 - #10 are more advanced, please note the extra instructions for them.
1. Ginger is a spice (G, S)
2. Jimmy Carter was not an academy award winner. (A)
3. Cell phones are not universally admired products. (C, U)
4. Some SUVs are not environmentally friendly vehicles. (B, C)
5. All whole numbers are either even or odd. (W, E, O)
6. Everything that is alive is mortal. (A, M)
Questions #7 - #10 are translations involving relational predicates, overlapping quantifiers, and identity. You can use the predicate letters provided.
7. Something destroyed everything. (Dxy: x destroyed y)
8. Everyone is a child of someone. (Cxy: x is a child of y)
9. Anyone who reads Kant reads Hume. (Rxy: x reads y, k: Kant, h: Hume)
10. Stan Lee invented Marvel Comics. (Ixm: x invented Marvel Comics; s: Stan Lee)
Proof of Validity Questions 11-14: (10 marks each) The following 4 arguments are valid. Provide a proof of validity for each argument. You can use the 18 rules of inference, CP, IP, the rules for introducing and removing quantifiers and the Change of Quantifier rules. Questions #13 #14 are more challenging, they involve relational predicates, overlapping quantifiers, and identity.
11.
1. ($x) Fx É ($x) (Gx • Hx)
2. ($x) Hx É (x) Jx \ (x) (Fx É Jx)
12.
1. (x) (Fx É Hx)
2. (x) (Fx É Gx) /\ (x) [ Fx É (Gx · Hx)]
13.
1. ($x) [Lx · (y) (My É Pxy)] /\ ($x) [Lx · (Mb É Pxb)]
14.
1. ~ Lb
2. (x) [ Hx É ( Lx · x = b)] /\ ~ Ha
Proving Invalidity Question 15: (10 marks) The following argument is invalid. Show it to be invalid using the finite universe method.
1. ($x) (Gx · Lx)
2. ($x) (Gx · Hx) /\ (x) (Lx É Hx)
This assignment, like all the assignments and term exams for this section of PHIL 1320, contains some questions from some of the following:
1. Baronett, Stan. Logic Second Edition. OUP. (New York: 2013) ISBN 978-0-19-984631-3.
2. Flage, Daniel E.. Understanding Logic. Prentice-Hall. (Englewood Cliffs New Jersey: 1995) ISBN 0-02-338173-6
3. Salmon, Merrilee H.. Introduction to Logic and Critical Thinking Third Edition. Harcourt Brace & Company. (Fort Worth: 1995) ISBN 0-15-543064-5
Order Notes
-
| Subject | Statistics | Pages | 5 | Style | APA |
|---|
Answer
Assignment 5
- Ginger is a spice (G, S)
(x) (Gx É Sx)
- Jimmy Carter was not an academy award winner. (A)
~ Ac
- Cell phones are not universally admired products. (C, U)
(x) (Cx É ~Ux)
- Some SUVs are not environmentally friendly vehicles. (B, C)
($x) (Bx · ~Cx)
- All whole numbers are either even or odd. (W, E, O)
(x) [Wx É (Ex v Ox)]
- Everything that is alive is mortal. (A, M)
(x) (Ax É Mx)
- Something destroyed everything. (Dxy: x destroyed y)
($x) (y) Dxy
- Everyone is a child of someone. (Cxy: x is a child of y)
(x) ($x) Cxy
- Anyone who reads Kant reads Hume. (Rxy: x reads y, k: Kant, h: Hume)
(x) (Rxk É Rxh)
- Stan Lee invented Marvel Comics. (Ixm: x invented Marvel Comics; s: Stan Lee)
($x) [ Ixm · (y) (Iym É y = x) · x = s]
11.
- (x) Fx É (x) (Gx • Hx)
- ($x) Hx É (x) Jx \ (x) (Fx É Jx)
- Fx ACP
- ($ x) Fx 3, EG
- ($ x) (Gx · Hx) 4,1 MP
- Gx & Hx 5, EI
- Hx & Gx 6, COM
- Hx 7, SIMP
- ($ x) Hx 8, EG
- (x) Jx 2,9 MP
- Jx 10, UI
- Fx É Jx 3 – 11 CP
- (x) (Fx É Jx) 12, UG
12.
- (x) (Fx É Hx)
- (x) (Fx É Gx) /\ (x) [ Fx É (Gx · Hx)]
- Fx ACP
- Fx É Gx 2, UI
- Fx É Hx 1, UI
- Gx 3,4 MP
- Hx 3, 5 MP
- Gx · Hx 6, 7 CONJ
- Fx É (Gx · Hx) 3-8 CP
- (x) [Fx É (Gx · Hx)] 9, UG
13.
- ($x) [Lx · (y) (My É Pxy)] /\ ($x) [Lx · (Mb É Pxb)]
- La · (y) (My É Pay) 1, EI
- La 2, SIMP
- (y) (My É Pay) · La 2, COM
- (y) (My É Pay) 4, SIMP
- Mb É Pab 5, UI
- La · (Mb É Pab) 3, 6 CONJ
- ($x) [Lx · (Mb É Pxb)] 7, EG
14.
- ~ Lb
- (x) [ Hx É ( Lx · x = b)] /\ ~ Ha
- Ha AIP
- Ha É (La · a=b) 2, UI
- La · a=b 3,4 MP
- La 5, SIMP
- a=b · La 5, COM
- a=b 7, SIMP
- Lb 6, 8 ID
- Lb · ~Lb 1, 9 CONJ
- ~ Ha 3-10 IP
15.
- ($x) (Gx · Lx)
- ($x) (Gx · Hx) /\ (x) (Lx É Hx)
A universe containing two individuals:
Ga = T La = T Ha = F
Gb = T Lb = T/F Hb = T
(Ga · La) v (Gb · Lb) / (Ga · Ha) v (Gb · Hb) // (La É Ha) · (Lb É Hb)
downsides, hence facilitating an effective engagement process.
References
|
Appendix
|
|