Q21,paper 3, d13. Given the following statements :

S1: The grammars S ->asb | bsa | ss | a and S ->asb | bsa | a are not equivalent.

S2: The grammars S ->ss | sss | asb | bsa | λ and S ->ss | asb | bsa | λ are equivalent.

Which of the following is true ?

(A) S1 is correct and S2 is not correct.

(B) Both S1and S2 are correct.

(C) S1is not correct and S2 is correct.

(D) Both S1 and S2 are not correct.

Answer B.

Explanation.

One length word generated by G1 in statement 1 .  {a}.

One length word generated by G2 in statement 1. {a}.

Two word length generated by G1 in statement 1. {aa}.

Two word length generated by G2 in statement 1.{}.

Hence we can say that two grammars are not equivalents.

Two length word generated  by G3, G4 in statement  s2. {ab,ba}.

Four length word generated by G3.

The grammars S ->ss | sss | asb | bsa | λ

S->ss->abab

S->ss->abba

s->ss->baab

s->ss->baba.

s->sss->abab,baab,baba,abba.

s->asb->aabb.

s->asb->abab

s->bsa->baba

s->bsa->bbaa

Four length words  generated by G4

S ->ss | asb | bsa | λ are same as above.