The Jabber-Notty
Can you invert this confusing sentence from Lewis Carrol?
Age
16 to 18
Challenge level
Problem
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.
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.
Student Solutions
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 brillig", 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 brillig".
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 brillig, or at least one slithy tove did not gyre and gimble in the wabe"
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 brillig", 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 brillig".
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 brillig, or at least one slithy tove did not gyre and gimble in the wabe"