# Defining nullable symbols and the first set of a grammar

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.