Question 1003230
<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>S &gt; (~U * B)</td><td></td><td></td></tr><tr><td>.:</td><td></td><td>(~H &gt; S) &gt; (~H &gt; B)</td><td></td><td></td></tr><tr><td>|</td><td>2</td><td>~H &gt; S</td><td></td><td>ACP</td></tr><tr><td>|</td><td>3</td><td>~H &gt; (~U * B)</td><td>2,1</td><td>HS</td></tr><tr><td>|</td><td>4</td><td>~~H v (~U * B)</td><td>3</td><td>MI</td></tr><tr><td>|</td><td>5</td><td>H v (~U * B)</td><td>4</td><td>DN</td></tr><tr><td>|</td><td>6</td><td>(H v ~U) * (H v B)</td><td>5</td><td>Dist</td></tr><tr><td>|</td><td>7</td><td>(H v B) * (H v ~U)</td><td>6</td><td>Comm</td></tr><tr><td>|</td><td>8</td><td>H v B</td><td>7</td><td>Simp</td></tr><tr><td>|</td><td>9</td><td>~~H v B</td><td>8</td><td>DN</td></tr><tr><td>|</td><td>10</td><td>~H &gt; B</td><td>9</td><td>MI</td></tr><tr><td>11</td><td></td><td>(~H &gt; S) &gt; (~H &gt; B)</td><td>2-10</td><td>CP</td></tr></table>


Acronyms/Abbreviations used:


ACP = Assumption for Conditional Proof
CP = Conditional Proof
HS = Hypothetical Syllogism
MI = Material Implication
DN = Double Negation
Comm = Commutation
Dist = Distribution
Simp = Simplification