How do I do this? You are given the following context$-$free grammar:

$SAB$

$A$ Aa$|$Bbla

$B$ Bb$|$Aalb

Part $1(1$ point$)$: Determine if the string "ababab" can be derived using the given grammar.

If the string can be derived, then provide the canonical derivation $($either left$-$most or right$-$

most, but not the combination of both$).$

If the string can be derived, then create a parse tree and an abstract syntax tree for this

string. Save the parse tree as problem$1\_$parse$\_$tree.jpg and the abstract syntax tree as

problem$1\_$abstract$\_$tree.jpg$.$

Answer the question: Is this string ambiguous? $($i$.$e$.,$ there should only be one valid parse tree

for it$).$ If yes, identify a string that can be derived from this grammar using two distinct parse

trees. Demonstrate the derivation for both parse trees. If not, explain why.

Part $2(1$ point$)$: Answer the question: Is this grammar ambiguous?

If yes, identify a string that can be derived from this grammar using two distinct parse trees.

Save these parse trees as problem$1\_$part$2\_$tree$1.$jpg and problem$1\_$part$2\_$tree$2.$jpg$.$

If no$,$ then prove that the grammar cannot produce more than one parse tree for any string

derived from the grammar. Use a deduction method to analyze different substrings $($e$.$g$.,$

"aaa", "aba", "abb", "bab", etc.$),$ demonstrating that each has only one valid parse tree.

Part $3(1$ point$)$: Can the string "aabb" be derived using this grammar?

If yes, show the parse tree. Save it as problem$1\_$part$3\_$tree.jpg$.$

If not, explain why it is impossible to derive this string from the given grammar.

Hint: To prove ambiguity, you must show two distinct $($i$.$e$.$ different$)$ trees that produce the same string

$($you can use non$-$canonical derivations in the proof$)$ or prove that no such derivations exist.