Characterizing the strings in a recursively defined set.

the recursive definition given below defines a set s of strings over the alphabet {a, b}:

base case: λ ∈ s and a ∈ s

recursive rule: if x ∈ s then,

xb ∈ s (rule 1)

xba ∈ s (rule 2)

(a)

use structural induction to prove that if a string x ∈ s, then x does not have two or more consecutive a's.