Question 1091271
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Note: I'm using the ampersand symbol & in place of the asterisk


This is one way to do the derivation
<table border=1 cellpadding=3><tr><th>Number</th><th>Statement</th><th>Lines Used</th><th>Reason</th></tr><tr><td>1</td><td>(D &amp; E) v (~D &amp; ~E)</td><td></td><td></td></tr><tr><td>2</td><td>(H &amp; J) &gt; ~(D = E)</td><td></td><td></td></tr><tr><td>3</td><td>~~H v J</td><td></td><td></td></tr><tr><td>:.</td><td>J = ~H</td><td></td><td></td></tr><tr><td>4</td><td>~H &gt; J</td><td>3</td><td>Material Implication</td></tr><tr><td>5</td><td>D = E</td><td>1</td><td>Material Equivalence</td></tr><tr><td>6</td><td>~~(D = E)</td><td>5</td><td>Double Negation</td></tr><tr><td>7</td><td>~(H &amp; J)</td><td>2,6</td><td>Modus Tollens</td></tr><tr><td>8</td><td>~H v ~J</td><td>7</td><td>De Morgan's Law</td></tr><tr><td>9</td><td>~J v ~H</td><td>8</td><td>Commutation</td></tr><tr><td>10</td><td>~~J &gt; ~H</td><td>9</td><td>Material Implication</td></tr><tr><td>11</td><td>J &gt; ~H</td><td>10</td><td>Double Negation</td></tr><tr><td>12</td><td>(J &gt; ~H) &amp; (~H &gt; J)</td><td>11,4</td><td>Conjunction</td></tr><tr><td>13</td><td>J = ~H</td><td>12</td><td>Material Equivalence</td></tr></table>
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