Question 1198762
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This is one way to do the derivation.
<table border = "1" cellpadding = "5"><tr><td colspan=2>Number</td><td>Statement</td><td>Line(s) Used</td><td>Reason</td></tr><tr><td>1</td><td></td><td>(P v F) ⊃ (A v D)</td><td></td><td></td></tr><tr><td>2</td><td></td><td>A ⊃ (M • ~P)</td><td></td><td></td></tr><tr><td>3</td><td></td><td>D ⊃ (C • ~P)</td><td></td><td></td></tr><tr><td colspan=2>:.</td><td>~P</td><td></td><td></td></tr><tr><td></td><td>4</td><td>~(~P)</td><td></td><td>Assumption For Indirect Proof</td></tr><tr><td></td><td>5</td><td>P</td><td>4</td><td>Double Negation</td></tr><tr><td></td><td>6</td><td>P v F</td><td>5</td><td>Addition</td></tr><tr><td></td><td>7</td><td>A v D</td><td>1,6</td><td>Modus Ponens</td></tr><tr><td></td><td>8</td><td>(M • ~P) v (C • ~P)</td><td>2,3,7</td><td>Constructive Dilemma</td></tr><tr><td></td><td>9</td><td>(M v C) • ~P</td><td>8</td><td>Distribution</td></tr><tr><td></td><td>10</td><td>~P</td><td>9</td><td>Simplification</td></tr><tr><td></td><td>11</td><td>~P • P</td><td>10,5</td><td>Conjunction</td></tr><tr><td>12</td><td></td><td>~P</td><td>4 - 11</td><td>Indirect Proof</td></tr></table>
The idea is to start with the conclusion ~P and negate it to get ~(~P).
The goal is to show a contradiction arises when we assume the opposite of the conclusion.
As shown above, the contradiction happens on line 11 when we have ~P and P together. 
This contradiction then leads us to conclude the opposite of the assumption ~(~P) must be the case, i.e. the original conclusion we started with is the case.
This fully wraps up the proof.
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