Consider the following grammar G: S → XC ∣ AY X → aXb ∣ ε C → cC ∣ ε Y → bYc ∣…

Final answer: The grammar is ambiguous and the language generated by it is also ambiguous (inherently ambiguous).

Explanation:

• Grammar ambiguity:

  For any n ≥ 0 the string a^n b^n c^n can be generated in two different ways:

  1. Using S → X C: X ⇒ a^n b^n and C ⇒ c^n, so S ⇒ X C ⇒ a^n b^n c^n.

  2. Using S → A Y: A ⇒ a^n and Y ⇒ b^n c^n, so S ⇒ A Y ⇒ a^n b^n c^n.

• Language ambiguity:

  Because the infinite family of strings {a^n b^n c^n | n ≥ 0} each has two distinct parse trees (one witnessing equality of the first two counts and the other witnessing equality of the last two counts), there are infinitely many strings with multiple parses. Therefore the language has no unambiguous grammar (it is inherently ambiguous).