Consider the context-free grammar:$$S\rightarrow SS + \mid SS {\ast} \mid a$$and the string $aa + a{\ast}$.
- Give a leftmost derivation for the string.
- Give a rightmost derivation for the string.
- Give a parse tree for the string.
- Is the grammar ambiguous or unambiguous? Justify your answer.
- Describe the language generated by this grammar.