SOLUTION: I need help solving this proof, please help! Premises: 1. A ⊃ (B⊃C) 2. A & ~C 3. (~B or D) ⊃ ~ (A&E) Conclusion: /~(C v E) Thanks in advance!

Algebra.Com
Question 969499: I need help solving this proof, please help!
Premises:
1. A ⊃ (B⊃C)
2. A & ~C
3. (~B or D) ⊃ ~ (A&E)
Conclusion:
/~(C v E)
Thanks in advance!
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
1. A ⊃ (B⊃C)
2. A & ~C
3. (~B v D) ⊃ ~ (A&E)
Conclusion:
/~(C v E) 
 4. A        simplification,2
 5. B⊃C      modus ponens,1,4
 6. ~C⊃~B    contrapositive,5
 7. ~C       simplification,2
 8. ~B       modus ponens,6,7
 9. ~B v D   disjunctive addition,8
10  ~(A&E)   modus ponens,3,9
11. ~Av~E    Demorgan's,10
12.  ~~A     double negation,4
13. ~E       disjunctive syllogism,11,12
14. ~C&~E    conjunction,7,13
15. ~(CvE)   Demorgan's,14

Edwin
RELATED QUESTIONS

Please help me solve this proof! Premises: 1. (A⊃B)&(C⊃D) 2.... (answered by Edwin McCravy)
Indirect proof 9. 1) R 2) (~ C v ~ D) v S 3) ~ (C ⋅ D) ⊃ ~R / ∴ S (answered by solver91311)
Please help! A ⊃ B A ⊃ (B ⊃ C) B ⊃ (C ⊃ D) ∴ A... (answered by Edwin McCravy)
Premises: 1. A ⊃ X 2. X ⊃ (B... (answered by math_helper)
Use natural deduction to derive the conclusion of the following arguments. Do not use... (answered by math_helper)
Using a conditional proof: 1. (D v E) ⊃ (F · G) 2.( A v B) ⊃ (D · C) (answered by jim_thompson5910)
Could you please help me? Im sick with a bug and cant think straight :/ A) 1. A ⊃ (answered by solver91311)
Using an indirect proof to solve this problem: 1. B ⊃ (C ⊃~B) 2. A... (answered by jim_thompson5910)
Does this proof look correct to you? If you notice any mistakes please let me know! Thank (answered by jim_thompson5910)