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| 78 views
0
D?
+3
option C

$X$ is recursive $\implies \bar X$ is also recursive.

$Y$ is r.e. but not recursive $\implies \bar Y$ is not even r.e.

$\bar X$ reduces to $W \implies$ $W$ is recursive or a super set of it.

$\bar Y$ reduces to $Z \implies$ $Z$ is not even r.e.

by Veteran (416k points)
selected
Compliment(REC)=REC                                                 X=REC

Compliment (RE but recursive) = RE

Compliment (RE but not recursive) = Not RE                     Y=RE but not REC

i.e W=Compliment(X)=REC

Z=Compliment(Y)=Not RE

D) is correct
by Active (1.1k points)
x complement recursive and y complement not RE hence option D
by (257 points)