Question $2.($e$)$

Suppose $$ is an input to a decision problem A and $$ is an input to decision problem $B$

Suppose also that a reduction algorithm, $R,$ that runs in polynomial time, transforms $$ into $$ and that $A()=B().$

Consider the case where $B$ is known to be complexity class $P.$ Explain why $A$ is also in complexity class $P.$

Fill in your answer here

Question $2,($f$)$

With reference to the above question part, consider now the situation where $A$ is known to be unsolvable in polynomial time but

the complexity class of $B$ is unknown. Show how the existence of $R$ is sufficient to prove that $B$ is not solvable in polynomial

time.