Q: Inductive Definition on the set of strings Given:
$$ \Sigma = \{ a, b, c \}. $$
I am trying to give the inductive definitions of both the set of strings $\Sigma^*$ and $\Sigma^+$.
Thank you.

A: The set $\Sigma^*$ contains all strings. The set $\Sigma^+$ contains all non-empty strings.
Your inductive definition of $\Sigma^*$ will go like this: a string is either empty or of the form $sa$ where $s$ is a string and $a$ is a character. So to form a string, you start with the empty string and keep adding characters at the end.
