Question 1005236
<table border=1><tr><th>Number</th><th>Statement</th><th>Lines Used</th><th>Reason</th></tr><tr><td>1</td><td>F &gt; ~G</td><td></td><td></td></tr><tr><td>2</td><td>~F &gt; (H &gt; ~G)</td><td></td><td></td></tr><tr><td>3</td><td>(~I v ~H) &gt; ~~G</td><td></td><td></td></tr><tr><td>4</td><td>~I</td><td></td><td></td></tr><tr><td>:.</td><td>~H</td><td></td><td></td></tr><tr><td>5</td><td>(~I v ~H) &gt; G</td><td>3</td><td>DN</td></tr><tr><td>6</td><td>~(~I v ~H) v G</td><td>5</td><td>MI</td></tr><tr><td>7</td><td>(~~I * ~~H) v G</td><td>6</td><td>DM</td></tr><tr><td>8</td><td>(I * H) v G</td><td>7</td><td>DN</td></tr><tr><td>9</td><td>G v (I * H)</td><td>8</td><td>Comm</td></tr><tr><td>10</td><td>(G v I) * (G v H)</td><td>9</td><td>Dist</td></tr><tr><td>11</td><td>G v I</td><td>10</td><td>Simp</td></tr><tr><td>12</td><td>I v G</td><td>11</td><td>Comm</td></tr><tr><td>13</td><td>G</td><td>12,4</td><td>DS</td></tr><tr><td>14</td><td>~~G</td><td>13</td><td>DN</td></tr><tr><td>15</td><td>~F</td><td>1,14</td><td>MT</td></tr><tr><td>16</td><td>H &gt; ~G</td><td>2,15</td><td>MP</td></tr><tr><td>17</td><td>~H</td><td>16,14</td><td>MT</td></tr></table>


Abbreviation/Acronyms Used


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