Solution

The correct answer is Option 2) C, D Only

What “only Context-Free” means

• A context-free grammar (CFG) has productions of the form V → α where the left side is a single variable and α is any string of variables/terminals.
• A regular grammar (a proper subset of CFGs) must be right-linear (V → a or V → aW) or left-linear (V → a or V → Wa) and must not mix both directions in one grammar. Regular grammars generate regular languages.
• “Only context-free” here means: context-free but not regular.

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Check each grammar

A. S → Ab

• Left linear: a variable followed by a terminal (Ab).
• This is consistent with a regular (left-linear) form. Even if there were no further rules (so the language is empty), the language is still regular. Hence not “only CF”.

B. S → Ab, aS → aA, A → Sa, A → a

• The production aS → aA has a left side that is not a single variable. Therefore this grammar is not context-free (it is an unrestricted/context-sensitive rule).
• So B cannot be “only CF”.

C. S → AS, S → aA

• Left sides are single variables ⇒ CFG.
• The rule S → AS contains two variables on the right; such a rule cannot appear in a regular grammar.
• Therefore C is context-free but not regular ⇒ only CF.

D. S → Ab, S → aA, A → a

• All left sides are single variables ⇒ CFG.
• It mixes left-linear (S → Ab) and right-linear (S → aA) forms in the same grammar. Such mixing in general yields a language that is not regular (unless in a trivial degenerate case).
• Hence D is context-free but not regular ⇒ only CF.

E. S → Sb, A → Aa, A → ε

• All productions are left-linear or ε; this is a regular grammar (generates a regular language). (If S is the start symbol, the language from S is empty; empty language is regular. If the start were A, it generates a*, also regular.)
• Therefore E is regular, not “only CF”.

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Conclusion

• The grammars that are context-free but not regular are C and D only.