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
| Number | Statement | Line(s) Used | Reason | | 1 | | ~A -> (B & C) | | | | 2 | | D -> ~C | | | | :. | D -> A | | | | 3 | D | | Assumption for Conditional Proof | | 4 | ~C | 2,3 | Modus Ponens | | 5 | ~C v ~B | 4 | Addition | | 6 | ~B v ~C | 5 | Commutation | | 7 | ~(B & C) | 6 | De Morgan’s Law | | 8 | ~~A | 1,7 | Modus Tollens | | 9 | A | 8 | Double Negation | | 10 | | D -> A | 3-9 | Conditional 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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