Proving a grammar ambiguous (and language equivalence): the dangling-else example

A CFG is ambiguous iff some string has two distinct leftmost derivations (equivalently, two distinct parse trees) — exhibit ONE such string to prove it. Ambiguity is a property of the grammar, not the language: two grammars can generate the same language while one is ambiguous and the other unambiguous, as the classic dangling-else grammar shows.