Question 1179972
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Edit: RBryant you are clearly using a conditional proof. I would hope that a tutor such as yourself should know this basic logic concept. 
If not then read this page
<a href = "http://intrologic.stanford.edu/chapters/chapter_05.html">http://intrologic.stanford.edu/chapters/chapter_05.html</a>
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The proof by tutor RBryant is correct, but the instructions specifically state to NOT use a conditional proof. 


The tutor Edwin has made an error. 
The simplification and addition rules cannot apply to a piece of the expression, but rather must apply to the entire line.


Refer to these rules of inference and replacement
<a href="https://logiccurriculum.com/2019/02/09/rules-for-proofs/">https://logiccurriculum.com/2019/02/09/rules-for-proofs/</a>


This is how I would go about the derivation.
<table border = "1" cellpadding = "5"><tr><td>Number</td><td>Statement</td><td>Line(s) Used</td><td>Reason</td></tr><tr><td>1</td><td>O -> (Q * N)</td><td></td><td></td></tr><tr><td>2</td><td>(N v E) -> S</td><td></td><td></td></tr><tr><td>:.</td><td>O -> S</td><td></td><td></td></tr><tr><td>3</td><td>~O v (Q * N)</td><td>1</td><td>Material Implication</td></tr><tr><td>4</td><td>(~O v Q) * (~O v N)</td><td>3</td><td>Distribution</td></tr><tr><td>5</td><td>~O v N</td><td>4</td><td>Simplification</td></tr><tr><td>6</td><td>(~O v N) v E</td><td>5</td><td>Addition</td></tr><tr><td>7</td><td>~O v (N v E)</td><td>6</td><td>Association</td></tr><tr><td>8</td><td>O -> (N v E)</td><td>7</td><td>Material Implication</td></tr><tr><td>9</td><td>O -> S</td><td>8,2</td><td>Hypothetical Syllogism</td></tr></table> 
I used an arrow symbol in place of a horseshoe.
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