Question 1009334
Proof by contradiction


<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>(F v G) v (A v ~B)</td><td></td><td></td></tr><tr><td>2</td><td></td><td>F -&gt; A</td><td></td><td></td></tr><tr><td>3</td><td></td><td>B -&gt; ~G</td><td></td><td></td></tr><tr><td>.:</td><td></td><td>A v ~B</td><td></td><td></td></tr><tr><td></td><td>5</td><td>~(A v ~B)</td><td></td><td>AIP</td></tr><tr><td></td><td>6</td><td>~A &amp; ~~B</td><td>5</td><td>DM</td></tr><tr><td></td><td>7</td><td>~A &amp; B</td><td>6</td><td>DN</td></tr><tr><td></td><td>8</td><td>B &amp; ~A</td><td>7</td><td>Comm</td></tr><tr><td></td><td>9</td><td>~A</td><td>7</td><td>Simp</td></tr><tr><td></td><td>10</td><td>B</td><td>8</td><td>Simp</td></tr><tr><td></td><td>11</td><td>~F</td><td>2,9</td><td>MT</td></tr><tr><td></td><td>12</td><td>~G</td><td>3,10</td><td>MP</td></tr><tr><td></td><td>13</td><td>~F &amp; ~G</td><td>11,12</td><td>Conj</td></tr><tr><td></td><td>14</td><td>~(F v G)</td><td>13</td><td>DM</td></tr><tr><td></td><td>15</td><td>A v ~B</td><td>1,14</td><td>DS</td></tr><tr><td></td><td>16</td><td>~B</td><td>15,9</td><td>DS</td></tr><tr><td></td><td>17</td><td>B &amp; ~B</td><td>10,16</td><td>Conj</td></tr><tr><td>18</td><td></td><td>A v ~B</td><td>5-17</td><td>IP</td></tr></table>


Acroynyms/Abbreviations used


AIP = assumption for indirect proof
Comm = commutation
Conj = conjunction
IP = indirect proof
DM = de morgan's law
DN = double negation
DS = disjunctive syllogism
MP = modus ponens
MT = modus tollens
Simp = simplification