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 ->  Proofs -> 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!      Log On


   

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) About Me  (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