Suppose problem A is NP$-$complete and problem B is in NP but is not necessarily

NP$-$complete. Which of the following statements is $($are$)$ necessarily true? Explain your

answers using the definitions of P$,$ NP$,$ and NP$-$complete.

$($a$)$ A polynomial$-$time algorithm for A implies P$=$NP$.$

$($b$)$ A polynomial$-$time algorithm for B implies P$=$NP$.$

$($c$)$ A polynomial$-$time algorithm for A implies a polynomial$-$time algorithm for B$.$