 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-1/4j/b/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

The first displayed tree supplies the productions

S \Rightarrow A S

and

S \Rightarrow AA

, as well as an

A

-parse tree producing

ab

. By assumption there is also an

A

-parse tree producing

baba

. Substitute these trees as follows:

S \Rightarrow A S \Rightarrow A (AA) \Rightarrow ab baba ab .

The resulting yield is

abbabaab \in L (G) .

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