Consider the grammar G1:

S | aS | aSbS

Which of the following is correct (for a choice to be correct, all propositions must be correct)?

a) The string aaabbbababaabba is not generated by the grammar.

b) a) G1 generates all and only the strings of a's and b's such that every prefix has at least as many a's as b's.

b) The following inductive hypothesis will prove it: For n less than k, G1 generates all and only the strings of a's and b's of length n such that every prefix has at least as many a's as b's.

c) a) G1 generates all and only the strings of a's and b's such that every prefix has at least as many a's as b's.

b) The inductive hypothesis to prove it is: For n < k, it holds that: For any word in G1, any prefix of length n, is such that all its prefixes contain at least as many a's as b's.

d) a) G1 generates all and only the strings of a's and b's such that every prefix has at least as many a's as b's.

b) The following inductive hypothesis will prove it: For n < k, it holds that: Any word in G1 of length n, is such that all its prefixes contain at least as many a's as b's.

Can you please answer this question with the steps. Thanks!!!