Question 1009036
I'm going to use a conditional proof. So that means we assume E is true (line 3). If we can show it leads to A (line 12), then E > A is true.


<table border=1><tr><th colspan="2">Number</th><th>Statement</th><th>Lines Used</th><th>Reason</th></tr><tr><td>1</td><td></td><td>~(A &amp; B) = ~C</td><td></td><td></td></tr><tr><td>2</td><td></td><td>(D v E) &gt; C</td><td></td><td></td></tr><tr><td>.:</td><td></td><td>E &gt; A</td><td></td><td></td></tr><tr><td></td><td>3</td><td>E</td><td></td><td>ACP</td></tr><tr><td></td><td>4</td><td>E v D</td><td>3</td><td>Add</td></tr><tr><td></td><td>5</td><td>D v E</td><td>4</td><td>Comm</td></tr><tr><td></td><td>6</td><td>C</td><td>2,5</td><td>MP</td></tr><tr><td></td><td>7</td><td>~~C</td><td>6</td><td>DN</td></tr><tr><td></td><td>8</td><td>[~(A &amp; B) &gt; ~C] &amp; [~C &gt; ~(A &amp; B)]</td><td>1</td><td>ME</td></tr><tr><td></td><td>9</td><td>~(A &amp; B) &gt; ~C</td><td>8</td><td>Simp</td></tr><tr><td></td><td>10</td><td>~~(A &amp; B)</td><td>9,7</td><td>MT</td></tr><tr><td></td><td>11</td><td>A &amp; B</td><td>10</td><td>DN</td></tr><tr><td></td><td>12</td><td>A</td><td>11</td><td>Simp</td></tr><tr><td>13</td><td></td><td>E &gt; A</td><td>3-12</td><td>CP</td></tr></table>


Abbreviations/Acronyms Used:


ACP = Assumption for Conditional Proof
Add = Addition
Comm = Commutation
CP = Conditional Proof
DN = Double Negation
ME = Material Equivalence
MP = Modus Ponens
MT = Modus Tollens
Simp = Simplification