TOC CFG

Question

If language $L=\{a^n b^n \mid n \geq 0\}$, then language $L^2$ is given by

• A. $\{a^{2n} b^{2n} \mid n \geq 0\}$
• B. $\{a^n b^n a^n b^n \mid n \geq 0\}$
• C. $\{a^n b^n \mid n \geq 0\}$
• D. $\{a^n b^n a^m b^m \mid n, m \geq 0\}$

Answer 1

Answer : D 

Your Given Language is L= {a^n b^n} where n>=0

Just for simplification we can break this down like this

L^2 ===> L.L ===> {a^n b^n where n>=0}.{a^m b^m where m>=0 } 

By doing this Language is not changed at all your given Language was DCFL .And it is still DCFL .Now we can combinedly write them down like this .

L^2 ={a^n b^n a^m b^m where m,n >=0}