Recursion for strings: Is this correct

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My question is pretty straightforward: Give a recursive definition for the set of all strings of a’s and b’s, where all the strings are of even length.

I have attempted to solve the above question and I was wondering if you could tell me if my solution is correct or on the right track.

Updated solution

Base: ∈ S

Recursion: if s ∈ S

aas ∈ S

abs ∈ S

bas ∈ S

bbs ∈ S