Let L$1,$ L$2,$ and L$3$ be languages defined over the alphabet $=\{a,b\},$ where

L$1$ consists of all possible strings over $$ except the strings w$1,$ w$2,..,$

w$100$; i$.$e$.,$ start with all possible strings over the alphabet, take out $100$

particular strings, and the remaining strings form the language $L1$;

L$2$ is recognized by an NFA; and

$L3$ is recognized by a PDA.

What type of language is $($L$1$ L$2)$L$3?$ Justify your answer.

Prove that $L=\{a^m{b}^k{c}^n|mkn\}($where $|w|a$ means the number of a$\text{'}$s in $w)$ is

recursively enumerable. Demonstrate the moves with the string instances:

b

i$.$ aaabbc

ii$.$ b$)$abbcc