I'm practicing for an upcoming exam and am being tripped up by a review problem. The problem gives the following grammar:
$$S \rightarrow AB\$$$ $$A \rightarrow \epsilon | a | (T)$$ $$T \rightarrow T, S | S$$ $$B \rightarrow b$$
As far as I can tell, the only nullable symbol is $A$. It is the only non-terminal whose production contains the null symbol $\epsilon$. I don't think $S$, which contains $A$ in it's production, is a nullable symbol since the same production also contains $B$, which is not a nullable symbol, and both $A$ and $B$ would need to be nullable for $S$ to also be nullable. Is $A$ really the only nullable symbol in this grammar, or am I misinformed?
As for the first set, frankly, I'm just having trouble following my professor's notes for creating the first set. Could anyone help here or point me to a good resource for this?
Thank you all so much.