Define a Set $S$ Recursively as Follows:
I $\epsilon \in S$ II RECURSION: If

Essay

Define a set $S$ recursively as follows:
I. BASIS: $\epsilon \in S$
II. RECURSION: If $s$ and $t$ are in $S$ , then
$\begin{array} { l l l l } \text { a. } 0 s \in S & \text { b. } s 0 \in S & \text { c. } 1 s 1 t \in S & \text { d. } s 1 t 1 \in S \end{array}$
III. RESTRICTION: No strings other than those derived from I and II are in $S$ . Use structural induction to prove that every string in $S$ contains an even number of l's.