$Note\ points\ for:\ A\ is\ reducible\ to\ B:\ A\rightarrow B$
$1)\ A\ is\ UD\rightarrow B\ is\ UD$
$2)\ B\ is\ D\rightarrow A\ is\ D$
$3)\ B\ is\ recursive\rightarrow A\ is\ recursive$
$4)\ B\ is\ RE\rightarrow A\ is\ RE$
$5)\ A\ is\ D\rightarrow B\ may\ or\ may\ not\ D$
$6)\ B\ is\ UD\rightarrow A\ may\ or\ may\ not\ UD$
$7)\ A\ is\ not\ recursive\rightarrow B\ also\ not\ recursive$
$8)\ A\ is\ not\ RE\rightarrow B\ also\ not\ RE$
$Y'\rightarrow W$
$Given\ Y\ is\ RE\ but\ not\ recursive\ .Hence\ Y'\ will\ be\ Non-RE$
$Look\ for\ point\ 8)$
$Z\rightarrow X'$
$Given\ X\ is\ Recursive .Hence\ X'\ will\ be\ Recursive$
$Look\ for\ point\ 3)$
$Ans:C$