Which of the following grammars are ambiguous?

Analysis of Grammar Ambiguity

A grammar is considered ambiguous if there exists at least one string that has more than one leftmost derivation or parse tree.

Option A generates strings of the form an bn. Each string has a unique derivation sequence, making this grammar unambiguous.

Option B allows multiple parse trees for expressions like id + id * id due to missing operator precedence rules. This creates ambiguity.

Option C allows derivation of strings like 'aa' via left recursion (S -> aS -> aa) or right recursion (S -> Sa -> aa). This results in ambiguity.

Option D generates strings of the form an. Each string length corresponds to a unique number of recursive steps, ensuring a single derivation tree.

Conclusion: Options B and C are ambiguous grammars.