Question 1010727
<table border=1><tr><th>Number</th><th>Statement</th><th>Lines Used</th><th>Reason</th></tr><tr><td>1</td><td>A -&gt; (Q v R)</td><td></td><td></td></tr><tr><td>2</td><td>(R &amp; Q) -&gt; B</td><td></td><td></td></tr><tr><td>3</td><td>A &amp; ~B</td><td></td><td></td></tr><tr><td>:.</td><td>R = ~Q</td><td></td><td></td></tr><tr><td>4</td><td>~B &amp; A</td><td>3</td><td>Commutation</td></tr><tr><td>5</td><td>A</td><td>3</td><td>Simplification</td></tr><tr><td>6</td><td>~B</td><td>4</td><td>Simplification</td></tr><tr><td>7</td><td>Q v R</td><td>1,5</td><td>Modus Ponens</td></tr><tr><td>8</td><td>~(R &amp; Q)</td><td>2,6</td><td>Modus Tollens</td></tr><tr><td>9</td><td>~R v ~Q</td><td>8</td><td>De Morgan's Law</td></tr><tr><td>10</td><td>R -&gt; ~Q</td><td>9</td><td>Material Implication</td></tr><tr><td>11</td><td>~~Q v R</td><td>7</td><td>Double Negation</td></tr><tr><td>12</td><td>~Q -&gt; R</td><td>11</td><td>Material Implication</td></tr><tr><td>13</td><td>(R -&gt; ~Q) &amp; (~Q -&gt; R)</td><td>10,12</td><td>Conjunction</td></tr><tr><td>14</td><td>R = ~Q</td><td>13</td><td>Material Equivalence</td></tr></table>