 \(A \oplus B\) is called the effective join of \(A\) and \(B\) as it encodes the “information” contained in \(A\) on the even members of \(A \oplus B\) and that contained \(B\) on its odd members. \(A \oplus B\) is c.e. if both \(A\) and \(B\) are. Suppose we also define the operation 