Combining Turing Machines $(10$ points$)($Graded for correctness$)$ Let $A,B,C$ be Turing$-($a$)$ giving an informal $($but sufficiently detailed ${?}^3)$ description of a decider for $A,$

$($b$)$ prove that the language of your $TM$ is indeed $A$

$($c$)$ prove that your $TM$ is a decider

recognizable languages over an alphabet $.$ Assume that

$ABC={}^{**},$ and

$AB=AC=BC=\frac{O}{?}.$

Prove that $A$ is Turing$-$decidable by