$2.$ Reductions $1(10$ points$)$:$($Graded for correctness$)$

Let S$2=\{$M$|$ M is a TM with input alphabet $\{0,1\}$ such that $|$L$($M$)|=2\},$ so S$2$ contains

all encodings of Turing machines whose languages contain exactly two strings in $\{0,1\}$

$$

$.$ Is S$2$

decidable? Is it recognizable? Is it corecognizable? Answer the questions, and prove your answer.