Question 981975
Alternative method


<table border=1><tr><th>Number</th><th>Statement</th><th>Lines Used</th><th>Reason</th></tr><tr><td>1</td><td>Q &gt; ~Q</td><td></td><td></td></tr><tr><td>2</td><td>~(G &amp; Q) &gt; U</td><td></td><td></td></tr><tr><td>:.</td><td>~(G &amp; ~U)</td><td></td><td></td></tr><tr><td>3</td><td>~Q v ~Q</td><td>1</td><td>Material Implication</td></tr><tr><td>4</td><td>~Q</td><td>3</td><td>Tautology</td></tr><tr><td>5</td><td>~~(G &amp; Q) v U</td><td>2</td><td>Material Implication</td></tr><tr><td>6</td><td>(G &amp; Q) v U</td><td>5</td><td>Double Negation</td></tr><tr><td>7</td><td>U v (G &amp; Q)</td><td>6</td><td>Commutation</td></tr><tr><td>8</td><td>(U v G) &amp; (U v Q)</td><td>7</td><td>Distribution</td></tr><tr><td>9</td><td>(U v Q) &amp; (U v G)</td><td>8</td><td>Commutation</td></tr><tr><td>10</td><td>U v Q</td><td>9</td><td>Simplification</td></tr><tr><td>11</td><td>U</td><td>10,4</td><td>Disjunctive Syllogism</td></tr><tr><td>12</td><td>U v ~G</td><td>11</td><td>Addition</td></tr><tr><td>13</td><td>~G v U</td><td>12</td><td>Commutation</td></tr><tr><td>14</td><td>~(~~G &amp; ~U)</td><td>13</td><td>De Morgan's Law</td></tr><tr><td>15</td><td>~(G &amp; ~U)</td><td>14</td><td>Double Negation</td></tr></table>