Q27,Paper 2,d13 The context free grammar for the

language L = {aⁿb^m | n ≤m + 3, n ≥0, m ≥0} is

(A)S ->aaa A;

 A ->aAb | B,

B ->Bb | λ

(B) S ->aaaA|λ

, A->aAb | B,

B ->Bb | λ

(C) S->aaaA | aa A | λ,

A ->aAb | B,

               B ->Bb| λ

(D) S ->aaaA | aa A | aA | λ

             , A →aAb | B, B ->Bb | λ

 Answer D.

Explanation.

For n=0 and m=0. L={aaa}

N=1 and m=1 , L={aaaab}

N=2 and m=2. L={aaaaabb}

N=3 and m=3 . L={aaaaaabbb}.

Option D. qualifies all the option.