Question 1171806: 1. W ⊃ (P v C)
2. ~P
3. W/C
I am trying to see how they were able to get the conclusion "C"
I think it should be
4. C modus ponens 1,2
But I am not sure if that is correct or if i am on the wrong path.
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
You have the right idea, but it will require two steps instead of one.
You can use Modus Ponens on lines 1 & 3 getting P v C as the result.
This is because we're told that "If W, then (P v C)" on line 1 and we know that W is the case on line 3. So that must mean (P v C) is the case as a result.
Afterward, we use disjunctive syllogism on the statements P v C and ~P (line 2)
Basically from P v C we know that either P is the case or C is. But line 2 says that ~P is the case, so we know that P isn't the case. That leaves C being the conclusion.
Here's the derivation table of the proof argument
| Number | Statement | Lines Used | Reason | | 1 | W -> (P v C) | | | | 2 | ~P | | | | 3 | W | | | | :. | C | | | | 4 | P v C | 1,3 | Modus Ponens | | 5 | C | 4,2 | Disjunctive Syllogism |
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