CS 390 Solutions to Homework 7

1. Basis Step: Prove that $P(\Lambda )$ holds.
Inductive Step: Assuming that $P(w)$ holds for an arbitrary string w, prove that $P(aw)$ and $P(bw)$ hold.

2. The children of $q$ are the members of the set $\delta (q, \Lambda )$.

3. Basis Step: Prove that S T (S)
Note that S T is the basis of (S T ). So in the basis step we prove that the elements of S T i.e. the seeds of (S T) belong to (S).

Inductive Step: Assuming that for an arbitrary q in (S T) and in (S), we need to prove that (q, ) (S)
For in the inductive step we need to prove that if any element q of (S T) belongs to (S), then its children also belong to (S). Since the children of an arbitrary element q are the members of $\delta (q, \Lambda )$, what we need is to prove that (q, ) (S)