Multiple choice

Which one of the following grammars generates the language $ L=\left \{ a^{i}b^{j}\mid i\neq j \right \}$?

  1. $S\rightarrow AC\mid CB$ $C\rightarrow aCb\mid a\mid b$ $A\rightarrow aA\mid \varepsilon$ $B\rightarrow Bb\mid \varepsilon$
  2. $S\rightarrow aS\mid Sb \mid a\mid b$
  3. $S\rightarrow AC\mid CB$ $C\rightarrow aCb\mid \varepsilon$ $A\rightarrow aA\mid \varepsilon$ $B\rightarrow Bb\mid \varepsilon$
  4. $S\rightarrow AC\mid CB$ $C\rightarrow aCb\mid \varepsilon$ $A\rightarrow aA\mid a$ $B\rightarrow Bb\mid b$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation