Question 981858
You made a typo on line 4. It should be ~I v W instead of ~I & W


<table border=1><tr><th>Number</th><th>Statement</th><th>Lines Used</th><th>Reason</th></tr><tr><td>1</td><td>I &gt; ( L &amp; W)</td><td></td><td></td></tr><tr><td>2</td><td>(~W &gt; H) &gt; S</td><td></td><td></td></tr><tr><td>:.</td><td>I &gt; S</td><td></td><td></td></tr><tr><td>4</td><td>~I v (L &amp; W)</td><td>1</td><td>Material Implication</td></tr><tr><td>5</td><td>(~I v L) &amp; (~I v W)</td><td>4</td><td>Distribution</td></tr><tr><td>6</td><td>(~I v W) &amp; (~I v L)</td><td>5</td><td>Commutation</td></tr><tr><td>7</td><td>~I v W</td><td>6</td><td>Simplification</td></tr><tr><td>8</td><td>~~I &gt; W</td><td>7</td><td>Material Implication</td></tr><tr><td>9</td><td>I &gt; W</td><td>8</td><td>Double Negation</td></tr><tr><td>10</td><td>~(~W &gt; H) v S</td><td>2</td><td>Material Implication</td></tr><tr><td>11</td><td>~(~~W v H) v S</td><td>10</td><td>Material Implication</td></tr><tr><td>12</td><td>~(W v H) v S</td><td>11</td><td>Double Negation</td></tr><tr><td>13</td><td>(~W &amp; ~H) v S</td><td>12</td><td>De Morgan's Law</td></tr><tr><td>14</td><td>S v (~W &amp; ~H)</td><td>13</td><td>Commutation</td></tr><tr><td>15</td><td>(S v ~W) &amp; (S v ~H)</td><td>14</td><td>Distribution</td></tr><tr><td>16</td><td>S v ~W</td><td>15</td><td>Simplification</td></tr><tr><td>17</td><td>~W v S</td><td>16</td><td>Commutation</td></tr><tr><td>18</td><td>~~W &gt; S</td><td>17</td><td>Material Implication</td></tr><tr><td>19</td><td>W &gt; S</td><td>18</td><td>Double Negation</td></tr><tr><td>20</td><td>I &gt; S</td><td>9,19</td><td>Hypothetical Syllogism</td></tr></table>