Please help me with this two homework questions, for each question, only choose 1 option and explain why, thanks!

1.

A derivation of a string of length n in a context-free grammar:

A) must involve exactly 2n 1 applications of rules for all n.

D) must involve at least n rules and at most 2n rules.

E) can involve any positive integer number of rules.

B) must involve exactly 2n 1 applications of rules, except possibly when n <= 5.

C) must involve at least n rules, but can involve an arbitrarily large number.

2. True or Flase

(1)When applying the pumping lemma for a language L, for a selected string s, as long as we can show that for one decomposition of the selected string s into uvxyz which fail to pump for the language, we then can conclude that the language L is not context-free.

(2)The language L= { { a , b } } is context-free.