When reviewing the solutions to an exercise of theoretical informatics, I was stumbling over something I don't understand.
Given a language $L = \{w \in \sum^*| \exists x\in \Sigma. |w|_x=0\}$ with $\Sigma = \{a,b,c\}$ you should draw an NFA. The following NFA was given in the solution: NFA
What I don't understand is, why the sample space, as the NFA suggests, isn't containing combinations from all letters (e.g. abc, cbba etc.). As I learned $\sum^* = \bigcup_{n\in \Bbb N}$$\sum^n$ and therefore shouldn't it be $\sum^*=\{\epsilon, a, b, c, aa, ab, ac, ba, bb, bc, ca, cb, cc, aaa, aab, aac, aba, abb,$ abc$, \ldots\}$?
Thanks in advance for clearing this out!
In that case, then your $NFA$ is correct, rather the one you linked in $wrong$.
Here is a better example:
And $q_0$ is starting state ... forgot to draw the arrow