Which of the following are context free ?

Question

$L1 = a^i b^i c^j$ such that i>=1 and j>=1

$L2 = a^i b^i c^j$ such that j>=1

$L3 = a^i b^i c^j$ such that i>=1

 

Answer is only L1. I think all 3 are CFL's.

Comments

Technically, all 3 are CFLs, but in the second and third languages they should have given the rang of i anf j respectively.

Answer 1

L1 is definitely CFL

but in case of L2 and L3

In L2=a^i b^i c^j such that j>=1

The condition of i is missing so we can assume any of the conditions i=j or i<=j or i>=j.Then L2 is not CFL

Even in L3 =a^i b^i c^j such that i>=1 can be done as L2

Hence, L1 is CFL

Comments

Correct observation.