Question 981101
<table border=1><tr><th>Number</th><th>Statement</th><th>Lines Used</th><th>Reason</th></tr><tr><td>1</td><td>V v H</td><td></td><td></td></tr><tr><td>2</td><td>~(V &amp; D)</td><td></td><td></td></tr><tr><td>3</td><td>~(D &amp; H)</td><td></td><td></td></tr><tr><td>:.</td><td>~(D &amp; O)</td><td></td><td></td></tr><tr><td>4</td><td>H v V</td><td>1</td><td>Commutation</td></tr><tr><td>5</td><td>~~H v V</td><td>4</td><td>Double Negation</td></tr><tr><td>6</td><td>~H -&gt; V</td><td>5</td><td>Material Implication</td></tr><tr><td>7</td><td>~V v ~D</td><td>2</td><td>De Morgan's Law</td></tr><tr><td>8</td><td>~~V -&gt; ~D</td><td>7</td><td>Material Implication</td></tr><tr><td>9</td><td>V -&gt; ~D</td><td>8</td><td>Double Negation</td></tr><tr><td>10</td><td>~H -&gt; ~D</td><td>6,9</td><td>Hypothetical Syllogism</td></tr><tr><td>11</td><td>~D v ~H</td><td>3</td><td>De Morgan's Law</td></tr><tr><td>12</td><td>~~D -&gt; ~H</td><td>11</td><td>Material Implication</td></tr><tr><td>13</td><td>D -&gt; ~H</td><td>12</td><td>Double Negation</td></tr><tr><td>14</td><td>D -&gt; ~D</td><td>13,10</td><td>Hypothetical Syllogism</td></tr><tr><td>15</td><td>~D v ~D</td><td>14</td><td>Material Implication</td></tr><tr><td>16</td><td>~D</td><td>15</td><td>Tautology</td></tr><tr><td>17</td><td>~D v ~O</td><td>16</td><td>Addition</td></tr><tr><td>18</td><td>~(D &amp; O)</td><td>17</td><td>De Morgan's Law</td></tr></table>