Final answer:
Yes, if a string has two distinct leftmost derivations, it results in two distinct parse trees. Distinct derivations mean different sequences of productions, which then results in different syntactic structures represented by the parse trees.
Step-by-step explanation:
If a string in a given grammar has two distinct leftmost derivations, it indeed implies that it has two distinct parse trees.
In formal language theory and computer science, a leftmost derivation in a context-free grammar is a derivation in which the leftmost nonterminal in a sentential form is always the first one to be replaced or rewritten.
When there are two different ways to replace this leftmost nonterminal, leading to different sets of productions being applied, this means that there are two distinct derivations.
The concept of a parse tree, or syntax tree, is a tree representation of the syntactic structure of a string according to a context-free grammar.
Each parse tree represents one leftmost derivation of the string.
So, if you have two distinct leftmost derivations, you will have two different parse trees, because the sequences of productions used in the derivations determine the tree structure.
It's worth noting that a grammar for which this situation can occur—that is, a grammar that can generate multiple different parse trees for a single string—is known as an ambiguous grammar.
Ambiguity in grammars is generally undesirable, especially in programming languages, because it can lead to confusion in understanding the structure and meaning of strings (like program statements).