Weekly Challenge 46: The Jabber-Notty

6531 /www/nrich/html/content/id/6531/ 1 2011-06-14T10:00:47 <mdoxml version="1.0"> <ul id="buttonBar"> <li> <a href="http://nrich.maths.org/6341&part=">Warm-up problem</a> </li> <li> <a href="http://nrich.maths.org/6332&part=">Try this next</a> </li> <li> <a href="https://nrich.maths.org/discus/messages/27/27.html?1274115048">Ask NRICH</a> </li> <li> <a href="http://nrich.maths.org/6023&part=">Read all about it</a> </li> <li> <a href="http://nrich.maths.org/6094">Last week's problem</a> </li> </ul> Lewis Carrol thought that (in Through the looking glass, and what Alice found there) 'Twas brillig, and the slithy toves Did gyre and gimble in the wabe' I disagree entirely. Construct the negation of this sentence to represent my view. Did you know... ? Lewis Carrol was a mathematician who delighted in logical games and wordplay. His books are full of the sorts of sentences which often amuse those with a good understanding of logic.  </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <table style="" border="1"> <tbody> <tr> <td align="center" bgcolor="#FFFFCC" bordercolor="#999999" style="font-style: italic;" width="125"><a href="http://nrich.maths.org/6341&part=">Warm-up problem</a></td> <td align="center" bgcolor="#FFCCFF" style="font-style: italic;" width="125"><a href="http://nrich.maths.org/6332&part=">Try this next</a></td> <td align="center" bgcolor="#33FF99" style="font-style: italic;" width="125"><a href="https://nrich.maths.org/discus/messages/27/27.html?1274115048">Ask NRICH</a></td> <td align="center" bgcolor="#CCCCCC" bordercolor="#999999" style="font-style: italic;" width="125"><a href="http://nrich.maths.org/6023&part=">Read all about it</a></td> <td align="center" bgcolor="#0099FF" style="font-style: italic;" width="125"><a href="http://nrich.maths.org/6094/solution">Last week's solution</a></td> <td>dfg</td> </tr> <tr> <td colspan="5" style=""> For this statement, we need not understand what a 'tove' or 'wabe' is, but we do need to understand the conjunctions (twas, and, in) and how negation affects them. We use De Morgan's Law, which says that for two statements A and B $$ \lnot(A\cap B) = \lnot(A) \cup \lnot(B) $$ So let us denote A as "it was great", and B as "the slithy toves Did gyre and gimble in the wabe". We then see that $\lnot A$ is the statement "it was not great". And $\lnot B$ is the statement "at least one slithy tove did not gyre and gimble in the wabe". Combining these together, we find that: "Either it was not great, or at least one slithy tove did not gyre and gimble in the wabe" </td> </tr> <tr> <td colspan="5" style="" width="600">sdf</td> <td>sdf</td> </tr> </tbody> </table> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <table border="0" padding="0"> <tbody> <tr> <td width="125" bgcolor="#ffffcc" align="center" style="font-style: italic;" bordercolor="#999999"><a href="http://nrich.maths.org/6341&part=">Warm-up problem</a></td> <td width="125" bgcolor="#ffccff" align="center" style="font-style: italic;"><a href="http://nrich.maths.org/6332&part=">Try this next</a></td> <td width="125" bgcolor="#33ff99" align="center" style="font-style: italic;"><a href="https://nrich.maths.org/discus/messages/27/27.html?1274115048"> Ask NRICH</a></td> <td width="125" bgcolor="#cccccc" align="center" style="font-style: italic;" bordercolor="#999999"><a href="http://nrich.maths.org/6023&part=">Read all about it</a></td> <td width="125" bgcolor="#0099ff" align="center" style="font-style: italic;"><a href="http://nrich.maths.org/6094&part=soln">Last week's solution</a></td> <td> </td> </tr> <tr> <td colspan="5"> For this statement, we need not understand what a 'tove' or 'wabe' is, but we do need to understand the conjunctions (twas, and, in) and how negation affects them. We use De Morgan's Law, which says that for two statements A and B $$ \lnot(A\cap B) = \lnot(A) \cup \lnot(B) $$ So let us denote A as "it was great", and B as "the slithy toves Did gyre and gimble in the wabe". We then see that $\lnot A$ is the statement "it was not great". And $\lnot B$ is the statement "at least one slithy tove did not gyre and gimble in the wabe". Combining these together, we find that: "Either it was not great, or at least one slithy tove did not gyre and gimble in the wabe" </td> </tr> <tr> <td width="600" colspan="5"> </td> <td> </td> </tr> </tbody> </table> </mdoxml> 2 3 0 0 0 0 1 Weekly Challenge 46: The Jabber-Notty Can you invert this confusing sentence from Lewis Carrol? Collections Weekly Challenge Decision Mathematics and Combinatorics Logic