$($a$)$ Suppose problem X is in class NP$,$ problem Y is in class P$,$ and X is polynomially reducible to Y$.$ Which must be true?

a$.$ Problem X is in class P$.$

b$.$ Problem X is NP$-$complete.

c$.$ Both of the above.

d$.$ None of the above.

$($b$)$ Suppose problem X is in class NP$,$ problem Y is NP$-$complete, and X is polynomially reducible to Y$.$ Which must be true?

a$.$ Problem X is in class P$.$

b$.$ Problem X is NP$-$complete.

c$.$ Both of the above.

d$.$ None of the above.

$($c$)$ Suppose problem X is NP$-$complete, problem Y is in class P$,$ and X is polynomially reducible to Y$.$ Which must be true?

a$.$ Problem X is in class P$.$

b$.$ Problem Y is NP$-$complete.

c$.$ P $=$ NP$.$

d$.$ All of the above.

e$.$ None of the above.