If A is a language, then PREFIX(A) is the language

{u | uv A for some string v}

(a) Prove that if A is decidable, then PREFIX(A) is Turing recognizable.

(b) Prove that if A is Turing recognizable, then PREFIX(A) is Turing recognizable. [Since every decidable language is Turing recognizable, this part implies the first part, but since the proof is harder, I made it a separate part.]