Problem 4

Apparently it is possible to use the pumping lemma directly
on this language L.   However, we think you'll find it easier
(and the Sipser example 1.76 more helpful) if you apply the
pumping lemma to the set complement of L.   Once you have shown
that the set complement of L is not regular, it should take
you about one sentence to explain why L can't be regular.

As we discussed in class (Sept 27th), many closure properties
are "if" statements which have to be applied in the correct
direction.   This normally requires using a proof by contradiction.
You don't need to worry about this subtlety for this problem,
because this closure property happens to be an "if and only if"
so it can be applied in either direction.