Intro to Logic Hello I am having trouble trying to prove this valid without usin
ID: 3583375 • Letter: I
Question
Intro to Logic
Hello I am having trouble trying to prove this valid without using CP,AP, IP. I have done this proof using AP and IP but my professor does not want me to.
Below is a screenshot of the orignial question
These are the 18 rules that I am able to use to solve this proof. I can not use AP, IP, or CP
1. Conjunction
2. simplification
3. addition
4. Constructive dilemma
5. disjunctive syllogism
6. Hypothetical syllogism
7. Modus Ponens
8. Modus Tollens
9. Double Negation
10. DeMorgan Theoreum
11.Commutation
12 Implication
13. Exportation
14. Tautology
15. Strategy
16. Contraposition
17. Distribution
18. Association
19.Universal Instantiation
20.Existential Instantiation
21. Universal Generalization
22. Existential Generalization
Here is the proof I did using AP, IP:
(3) P (Ex) AxExplanation / Answer
I.
1. (x)[Ax: v (Bx v Cx)]
2. (3x)(Ax . -Cx) / (x)Bx
3. Am. -Cm 2, EI
4. Am V (Em v Cm) 1, UI
5. Am 3, Simp
6. Bm v Cm 4, 5, MP
7. -Cm 3, Com, Simp
8. Bm 6, 7, Com, DS
9. (x)Bx 8, EG
II.
1. (x)Ax › (x)(Bx ›Cx)
2. (x)Dx › (3x)~Cx
3. (x)(Ax . Ox) / (3x)-Bx
4. Am . Dm 3, EI
5. Am 4, Simp
6. Dm 4, Com, Simp
7. (x)Ax 5, EG
8. (x)Dx 6, EG
9. (x)(Bx › Cx) 1, 7, MP
10. (x)~Cx 2, 8, MP
11. ~Cn 10, EI
I2.Bn~Cn 9, VI
13. ~ Bn 11, 12, MT
14. (x)~Bx 13, EG
III.
1. (x)()(Ax:) -Ax) / -(x)Axx
2. (A:) -Am) 1, EI
3. Am:)-Am 2,UI
4. -Am v -Am 3, Impl
5. -Am 4, Taut
6. (x)-Ax 5, EG
7. -(x)Ax 6, CQ
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