Question 1201683
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<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>~N -> [ (B -> D) -> (N v ~E) ]</td><td></td><td></td></tr><tr><td>2</td><td>(B -> E) -> ~N</td><td></td><td></td></tr><tr><td>3</td><td>B -> D</td><td></td><td></td></tr><tr><td>4</td><td>D -> E</td><td></td><td></td></tr><tr><td>:.</td><td>~D</td><td></td><td></td></tr><tr><td>5</td><td>B -> E</td><td>3,4</td><td>Hypothetical Syllogism</td></tr><tr><td>6</td><td>~N</td><td>2,5</td><td>Modus Ponens</td></tr><tr><td>7</td><td>(B -> D) -> (N v ~E)</td><td>1,6</td><td>Modus Ponens</td></tr><tr><td>8</td><td>N v ~E</td><td>7,3</td><td>Modus Ponens</td></tr><tr><td>9</td><td>~E</td><td>8,6</td><td>Disjunctive Syllogism</td></tr><tr><td>10</td><td>~D</td><td>4,9</td><td>Modus Tollens</td></tr></table>
I used arrows in place of the horseshoe symbols.


For more information, check out the various rules of inference and rules of replacement as shown in the link below.
<a href = "https://logiccurriculum.com/2019/02/09/rules-for-proofs/">https://logiccurriculum.com/2019/02/09/rules-for-proofs/</a>


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