context-free-language

Question

A CFG G is ambiguous which of the following is false?

a) at least one w ∈ L(G) such that w has at least 2 distinct derivation trees

b) at least one w ∈ L(G) such that w has at least 2 RMD's and at least 2 LMD's

c) at least one w ∈ L(G) such that w has exactly 2 derivation trees

d)None of these

Comments

c???

---

Yes answer is C, but can you explain?

Answer 1

Statement 1: it is true as per definition of ambiguous gammer.

Statement 2: it is true because each LMD can be represented as a RMD vice versa. so as we have atleast two parse tree for a string we will have 2 LMD and 2 RMD minimum.

Statement 3: is is saying that a string   w has exactly 2 derivation trees  but suppose our language has 3 string in which two have unique parse tree but one has 3 derivation so it will not have exactly 2 parse tree.