SOLUTION: Can you please help me solve this proof? I am stuck at line six. 1. (A → E) → (D ∨ C) 2. D → (~B → C) ∴ ~C

Algebra.Com
Question 1009274: Can you please help me solve this proof? I am stuck at line six.
1. (A → E) → (D ∨ C)
2. D → (~B → C) ∴ ~C → (A ∨ B)
|3. ~C Assume
||4. ~A Assume
||5. (D∙~B)→C 2, EX
||6.
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
The idea is to assume ~C is true (line 3). Using the rules of inference/replacement, if we can lead to A v B somehow (line 25), then that proves ~C -> (A v B) is true.

NumberStatementLines UsedReason
1(A -> E) -> (D v C)
2D -> (~B -> C)
:.~C -> (A v B)
3~CACP
4(D & ~B) -> C2EXP
5~(D & ~B)4,3MT
6~D v ~~B5DM
7~D v B6DN
8D -> B7MI
9~B -> ~D8Trans
10~(A -> E) v (D v C)1MI
11~(~A v E) v (D v C)10MI
12(~~A & ~E) v (D v C)11DM
13(A & ~E) v (D v C)12DN
14(D v C) v (A & ~E)13Comm
15[(D v C) v A] & [(D v C) v ~E]14Dist
16(D v C) v A15Simp
17(C v D) v A16Comm
18C v (D v A)17Assoc
19D v A18,3DS
20~~D v A19DN
21~D -> A20MI
22~B -> A9,21HS
23~~B v A22MI
24B v A23DN
25A v B24Comm
26~C -> (A v B)3-25CP


Acroynyms/Abbreviations used

ACP = assumption for conditional proof
Assoc = associative property
Comm = commutation
CP = conditional proof
Dist = distribution
DM = de morgan's law
DN = double negation
DS = disjunctive syllogism
EXP = exportation
HS = hypothetical syllogism
MI = material implication
MT = modus tollens
Simp = simplification
Trans = transposition
RELATED QUESTIONS

1. A→B 2. A→~(C∨B) ∴ ~A 1. (A&~B)&(~C∨D) 2.... (answered by Edwin McCravy)
Please help with this proof. Thank You C→(D→H) D∙~H HvT ∴... (answered by jim_thompson5910)
Prove This: 1. B∨~C 2. B→E 3. ~~C... (answered by jim_thompson5910)
I AM STUCK NOW. 12. (A → B) & (A → C) ├ A→ (B & C) 1) (A... (answered by jim_thompson5910)
I need to help on the following proofs Proof 1 B ∧ F ¬(B ∧ G)... (answered by Edwin McCravy)
write a direct proof using the eight rules of inference (C → Q) • (~L →... (answered by Edwin McCravy)
Can you please help me complete the following rules by adding the implication rules to... (answered by robertb)
Please help me solve this logic proof: 1. E→H 2. (E ∨ F) • (E ∨ G) (answered by jim_thompson5910)
6) I can only use the 8 rules of inference... 1. (~B • ~C) → (D → C) 2. ~B (answered by jim_thompson5910)