SOLUTION: I need help deriving the conclusion (using CONDITIONAL proof). You can use all 18 rules. 1. (AvB)⊃(CvD) 2. (CvE)⊃D /A⊃D

Algebra ->  Proofs -> SOLUTION: I need help deriving the conclusion (using CONDITIONAL proof). You can use all 18 rules. 1. (AvB)⊃(CvD) 2. (CvE)⊃D /A⊃D      Log On


   

Question 1004972: I need help deriving the conclusion (using CONDITIONAL proof). You can use all 18 rules.
1. (AvB)⊃(CvD)
2. (CvE)⊃D /A⊃D
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: I'm going to use the symbol -> in place of the horseshoe symbol.


NumberStatementLines UsedReason
1(A v B) -> (C v D)
2(C v E) -> D
:.A -> D
|3AACP
|4A v B3Add
|5C v D1,4MP
|6D v C5Comm
|7~~D v C6DN
|8~D -> C7MI
|9~(C v E) v D2MI
|10(~C * ~E) v D9DM
|11D v (~C * ~E)10Comm
|12(D v ~C) * (D v ~E)11Dist
|13D v ~C12Simp
|14~C v D13Comm
|15C -> D14MI
|16~D -> D8,15HS
|17~~D v D16MI
|18D v D17DN
|19D18Taut
20A -> D3-19CP


Abbreviations/Acronyms Used

ACP = Assumption for Conditional Proof
Add = Addition
Comm = Commutation
CP = Conditional Proof
Dist = Distribution
DM = De Morgan's Law
DN = Double Negation
HS = Hypothetical Syllogism
MI = Material Implication
MP = Modus Ponens
Simp = Simplification
Taut = Tautology