# The Jabber-Notty

Can you invert this confusing sentence from Lewis Carrol?

## 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"