SOLUTION: Using an indirect proof to solve this problem: 1. B ⊃ (C ⊃~B) 2. A ⊃ (B ⊃ C) /~A v ~ B Thank you!

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Question 1060204: Using an indirect proof to solve this problem:
1. B ⊃ (C ⊃~B)
2. A ⊃ (B ⊃ C) /~A v ~ B

Thank you!

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
The idea is to assume the complete opposite of the conclusion (statement 3).
Then show how that assumption leads to to a contradiction (statement 14).
This contradiction means that the opposite of the assumption must be true. In other words, the original conclusion is true.

NumberStatementLines UsedReason
1B -> (C -> ~B)
2A -> (B -> C)
:.~A v ~B
3~(~A v ~B)AIP
4~~A & ~~B3DM
5A & B4DN
6B & A5Comm
7A5Simp
8B6Simp
9C -> ~B1,8MP
10B -> C2,7MP
11B -> ~B10,9HS
12~B v ~B11MI
13~B12Taut
14B & ~B8,13Conj
15~A v ~B3-14IP


Abbreviations/Acronyms Used
AIP = Assumption for Indirect Proof
Comm = Commutation
Conj = Conjunction
DM = De Morgan's Law
DN = Double Negation
HS = Hypothetical Syllogism
IP = Indirect Proof
MI = Material Implication
MP = Modus Ponens
Simp = Simplification
Taut = Tautology
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