Question 981173
Abbreviations/Acronyms Used:


Add = Addition
Comm = Commutation
DM = De Morgan's Law
DN = Double Negation
DS = Disjunctive Syllogism
MP = Modus Ponens
MT = Modus Tollens
Simp = Simplification


<table border=1><tr><th>Number</th><th>Statement</th><th>Lines Used</th><th>Reason</th></tr><tr><td>1</td><td>~(L v ~Z) &amp; B</td><td></td><td></td></tr><tr><td>2</td><td>(O &amp; Z) &gt; L</td><td></td><td></td></tr><tr><td>3</td><td>(~O v R) &gt; ~G</td><td></td><td></td></tr><tr><td>:.</td><td>~G</td><td></td><td></td></tr><tr><td>4</td><td>~(L v ~Z)</td><td>1</td><td>Simp</td></tr><tr><td>5</td><td>~L &amp; ~~Z</td><td>4</td><td>DM</td></tr><tr><td>6</td><td>~L &amp; Z</td><td>5</td><td>DN</td></tr><tr><td>7</td><td>~L</td><td>6</td><td>Simp</td></tr><tr><td>8</td><td>~(O &amp; Z)</td><td>2,7</td><td>MT</td></tr><tr><td>9</td><td>~O v ~Z</td><td>8</td><td>DM</td></tr><tr><td>10</td><td>Z &amp; ~L</td><td>6</td><td>Comm</td></tr><tr><td>11</td><td>Z</td><td>10</td><td>Simp</td></tr><tr><td>12</td><td>~~Z</td><td>11</td><td>DN</td></tr><tr><td>13</td><td>~Z v ~O</td><td>9</td><td>Comm</td></tr><tr><td>14</td><td>~O</td><td>13,12</td><td>DS</td></tr><tr><td>15</td><td>~O v R</td><td>14</td><td>Add</td></tr><tr><td>16</td><td>~G</td><td>3,15</td><td>MP</td></tr></table>