Re: separating context-free languages by simpler languages

And two more questions:

Is there a pair of two disjoint context-free languages (L1, L2) so that
neither L1 nor L2 is deterministic context-free, but

(a)
there is no pair of disjoint regular languages (R1, R2) with Li subset
Ri (i=1,2).

(b)
there is no pair of disjoint deterministic context-free languages
(D1, D2) with Li subset Di (i=1,2).
.