Consider the following two statements:

P: Every regular grammar is LL(1)
Q: Every regular set has a LR(1) grammar

Which of the following is TRUE?

Consider the grammar with non-terminals N = { S, C, S₁ }, terminals T = { a, b, i, t, e }, with S as the start symbol, and the following set of rules:

$$\eqalign{ & S \to iCtS{S_1}\,|\,\,a \cr & {S_1} \to eS\,|\,\,\varepsilon \cr & C \to b \cr} $$

The grammar is NOT LL(1) because:

Consider the CFG with { S, A, B } as the non-terminal alphabet, { a, b } as the terminal alphabet, S as the start symbol and the following set of production rules:

$$\eqalign{ & S \to bA\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,S \to aB \cr & A \to a\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,B \to b \cr & A \to aS\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,B \to bS \cr & S \to bAA\,\,\,\,\,\,\,\,\,\,\,B \to aBB \cr} $$

Which of the following strings is generated by the grammar?

Consider the CFG with { S, A, B } as the non-terminal alphabet, { a, b } as the terminal alphabet, S as the start symbol and the following set of production rules:

$$\eqalign{ & S \to bA\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,S \to aB \cr & A \to a\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,B \to b \cr & A \to aS\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,B \to bS \cr & S \to bAA\,\,\,\,\,\,\,\,\,\,\,B \to aBB \cr} $$

For the correct answer strings to the previous question, how many derivation trees are there?