SOLUTION: Prove the following using conditional proof: 1. ∼A ⊃ (B • C) 2. D ⊃ ∼C / D ⊃ A

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Question 1193420: Prove the following using conditional proof:
1. ∼A ⊃ (B • C)
2. D ⊃ ∼C / D ⊃ A
Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

Derivation Table
NumberStatementLine(s) UsedReason
1~A -> (B & C)
2D -> ~C
:.D -> A
3DAssumption for Conditional Proof
4~C2,3Modus Ponens
5~C v ~B4Addition
6~B v ~C5Commutation
7~(B & C)6De Morgan’s Law
8~~A1,7Modus Tollens
9A8Double Negation
10D -> A3-9Conditional Proof


In line 3, I have the antecedent D as the assumption to start the conditional proof off.
We simply start with the "if" part of the "if, then" conditional in the conclusion.
So we assume that the logical statement D is the case.
Somehow we have to arrive at statement A based on this key assumption.

That's exactly what this derivation table does. The proof more or less starts at line 3, while working its way down until reaching line 9 where we arrive at statement A.
Collectively lines 3 through 9 all group together to show D leading to A, therefore D -> A

I'm using arrow symbols in place of the horseshoe symbols.
Also, I used ampersands in place of the dot symbols.
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