(a) Define what it means for a context-free grammar (CFG) to be in Chomsky normal form ( $\mathrm{CNF})$.

(b) Give an algorithm for converting a CFG $G$ into a corresponding CFG $G_{\text {Chom }}$ in CNF satisfying $\mathcal{L}\left(G_{\text {Chom }}\right)=\mathcal{L}(G)-\{\epsilon\}$. [You need only outline the steps, without proof.]

(c) Convert the following $\mathrm{CFG} G$ :

$$S \rightarrow A S c \mid B, \quad A \rightarrow a, \quad B \rightarrow b$$

into a grammar in CNF.