The Jabber-notty

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"