Question 1088315
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<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>~F v ~G</td><td></td><td></td></tr><tr><td>2</td><td>~F &#8835; Z</td><td></td><td></td></tr><tr><td>3</td><td>~G &#8835; ~R</td><td></td><td></td></tr><tr><td>4</td><td>(Z v ~R) &#8835; (U &#8835; P)</td><td></td><td></td></tr><tr><td>5</td><td>~P</td><td></td><td></td></tr><tr><td>:.</td><td>~U</td><td></td><td></td></tr><tr><td>6</td><td>~~F &#8835; ~G</td><td>1</td><td>Material Implication</td></tr><tr><td>7</td><td>F &#8835; ~G</td><td>6</td><td>Double Negation</td></tr><tr><td>8</td><td>F &#8835; ~R</td><td>7,3</td><td>Hypothetical Syllogism</td></tr><tr><td>9</td><td>~Z &#8835; ~~F</td><td>2</td><td>Transposition</td></tr><tr><td>10</td><td>~Z &#8835; F</td><td>9</td><td>Double Negation</td></tr><tr><td>11</td><td>~Z &#8835; ~R</td><td>10,8</td><td>Hypothetical Syllogism</td></tr><tr><td>12</td><td>~~Z v ~R</td><td>11</td><td>Material Implication</td></tr><tr><td>13</td><td>Z v ~R</td><td>12</td><td>Double Negation</td></tr><tr><td>14</td><td>U &#8835; P</td><td>4,13</td><td>Modus Ponens</td></tr><tr><td>15</td><td>~U</td><td>14,5</td><td>Modus Tollens</td></tr></table>
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