Question 1155133
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I'm going to use an ampersand symbol in place of a dot.
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<tr><td>Number</td><td>Statement</td><td>Line(s) Used</td><td>Reason</td></tr>
<tr><td>1</td><td>K v (S & N)</td><td></td><td></td></tr>
<tr><td>2</td><td>~(K & ~Q)</td><td></td><td></td></tr>
<tr><td>3</td><td>~(N & ~Q)</td><td></td><td></td></tr>
<tr><td>Conclusion</td><td>Q</td><td></td><td></td></tr>
<tr><td>4</td><td>(K v S) & (K v N)</td><td>1</td><td>Distribution</td></tr>
<tr><td>5</td><td>(K v N) & (K v S)</td><td>4</td><td>Commutation</td></tr>
<tr><td>6</td><td>K v N</td><td>5</td><td>Simplification</td></tr>
<tr><td>7</td><td>~K v ~~Q</td><td>2</td><td>De Morgan’s Law</td></tr>
<tr><td>8</td><td>~K v Q</td><td>7</td><td>Double Negation</td></tr>
<tr><td>9</td><td>~N v ~~Q</td><td>3</td><td>De Morgan’s Law</td></tr>
<tr><td>10</td><td>~N v Q</td><td>9</td><td>Double Negation</td></tr>
<tr><td>11</td><td>K -> Q</td><td>8</td><td>Material Implication</td></tr>
<tr><td>12</td><td>N -> Q</td><td>10</td><td>Material Implication</td></tr>
<tr><td>13</td><td>(K -> Q) & (N -> Q)</td><td>11,12</td><td>Conjunction</td></tr>
<tr><td>14</td><td>Q v Q</td><td>13,6</td><td>Constructive Dilemma</td></tr>
<tr><td>15</td><td>Q</td><td>14</td><td>Tautology</td></tr>
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