CFL or not

Question

It seemed like , this is textbook example of non-CFL language ; will require 2 comparisons . That means no complement exist was the answer , I was expecting. Why answer given is CFL , am I missing something ?

Answer 1

Given language is L=aⁿbⁿcⁿ; {no. of a = no of b = no. of c}

complement of L is : {no. of a not equals no. of b OR no. of b not equals no. of c OR  no. of c not equals no. of a}

so there are two comparisons with unions.

Hence It is CFL.

Answer 2

complement of the given language will be $\bar{L}= {a^{l}b^{m}c^{n}| l!=m  or  m!=n}$

this language is cfl as you have to design to paths for the OR conditions.

Answer 3

Above languages is nothing but context sensitive language.

Since we know that CSL is closed under the intersection as well as complementation therefore it must be CSL therefore by extension it must be CFL ,as well as DCFL and RL..

So option of CFL and DCFL will be right.