Possible strings in transition diagrams for DFAs.

Possible strings in transition diagrams for DFAs.


Hi, my question is, in these questions, what are u and w exactly. Ie, what
are the values they can take. I can't draw the transition diagram without
knowing them.
From what I understand, the $\Sigma^*$ symbol is the set of all subsets of
$\Sigma$={a, b} which I think would be {Ø, a, b, ab}. So if u and w are
members of $\Sigma^*$, does that mean they can take any of those values?
So for example, in a) could the possible strings be... a, aa, ab, aab?
Any help would be appreciated because I cant draw the transition diagrams
without knowing this.