SOLUTION: I need help with proofs. Thank you!
D →(B→C), B & −C ├ −D
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Question 978498: I need help with proofs. Thank you!
D →(B→C), B & −C ├ −D
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
You can do a proof by contradiction.
Step 1) Assume the opposite of the conclusion. Assume ~~D which is equivalent to D
Step 2) Since we have D, we can use D -> (B -> C) and modus ponens to get B -> C
Step 3) Use simplification to go from B & ~C to just B. You can also free up ~C as well
Step 4) Use B and B -> C to get C (modus ponens again)
Step 5) The ~C and C contradict one another. So the original assumption is not possible. Therefore, the opposite of the assumption (D) is the only possibility.
So that's one way we can prove that ~D is the conclusion.
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