Question: Let a and b be two characters. Define, recursively, a set S of strings by: 1 S (where is the empty string) 2 if x

Let a and b be two characters. Define, recursively, a set S of strings by:

1 S (where is the empty string)

2 if x S, then xa S

if x S, then bbx S,

where xa and bbx represents concatenation of strings/characters.

Prove, using structural induction, that x S, m, n integers, m, n 0,

so that x = bb b (2m times) aa a (n times)

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