Given a language L, let PREFIX(L) be the language of prefixes for words in L.

i.e. PREFIX(L) = {x | there exists y such that xy ? L}

Prove or disprove:

(a) RE is closed under prefix.

(b) R is closed under prefix.

(Notation:

RE - Recursively Enumerable - Turing-Recognizable Language

R - Recursive - Turing-Decidable Language)