Question 1171806
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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
<table border = "1" cellpadding = "5"><tr><td>Number</td><td>Statement</td><td>Lines Used</td><td>Reason</td></tr><tr><td>1</td><td>W -> (P v C)</td><td></td><td></td></tr><tr><td>2</td><td>~P</td><td></td><td></td></tr><tr><td>3</td><td>W</td><td></td><td></td></tr><tr><td>:.</td><td>C</td><td></td><td></td></tr><tr><td>4</td><td>P v C</td><td>1,3</td><td>Modus Ponens</td></tr><tr><td>5</td><td>C</td><td>4,2</td><td>Disjunctive Syllogism</td></tr></table>

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