Question 1061182
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<table border=1 cellpadding=3><tr><th>Number</th><th>Statement</th><th>Lines Used</th><th>Reason</th></tr><tr><td>1</td><td>(N v M) &gt; (P &amp; O)</td><td></td><td></td></tr><tr><td>2</td><td>~M &gt; (~Q &gt; Q)</td><td></td><td></td></tr><tr><td>3</td><td>~O</td><td></td><td></td></tr><tr><td>:.</td><td>Q</td><td></td><td></td></tr><tr><td>4</td><td>~(N v M) v (P &amp; O)</td><td>1</td><td>MI</td></tr><tr><td>5</td><td>[~(N v M) v P] &amp; [~(N v M) v O]</td><td>4</td><td>Dist</td></tr><tr><td>6</td><td>[~(N v M) v O] &amp; [~(N v M) v P]</td><td>5</td><td>Comm</td></tr><tr><td>7</td><td>~(N v M) v O</td><td>6</td><td>Simp</td></tr><tr><td>8</td><td>O v ~(N v M)</td><td>7</td><td>Comm</td></tr><tr><td>9</td><td>~(N v M)</td><td>8,3</td><td>DS</td></tr><tr><td>10</td><td>~N &amp; ~M</td><td>9</td><td>DM</td></tr><tr><td>11</td><td>~M &amp; ~N</td><td>10</td><td>Comm</td></tr><tr><td>12</td><td>~M</td><td>11</td><td>Simp</td></tr><tr><td>13</td><td>~M &gt; (~~Q v Q)</td><td>2</td><td>MI</td></tr><tr><td>14</td><td>~M &gt; (Q v Q)</td><td>13</td><td>DN</td></tr><tr><td>15</td><td>~M &gt; Q</td><td>14</td><td>Taut</td></tr><tr><td>16</td><td>Q</td><td>15,12</td><td>MP</td></tr></table>

Abbreviations/Acronyms used:


Comm = Commutation
Dist = Distribution
DM = De Morgan's Law
DN = Double Negation
DS = Disjunctive Syllogism
MI = Material Implication
MP = Modus Ponens
Simp = Simplification
Taut = Tautology
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