This question is about complexity.

$($a$)$ What is the difference between complexity class $P^{\text{W}\text{H}\text{I}\text{L}\text{E}}$ and $N{P}^{\text{W}\text{H}\text{I}\text{L}\text{E}}.$

$($b$)$ For EACH of the statements below state whether it is known to be true, known

to be false, or whether it is unknown whether it is true or false. You do not have

to give reasons for your answer.

i$.P^{TM}=P^{\text{R}\text{a}\text{M}}.$

ii$.$ The Parsing Problem is in NP$.$

iii. $P^{\text{R}\text{A}\text{M}}=N{P}^{\text{V}\text{H}\text{I}\text{L}\text{E}}$

iv$.$ Worst case array sorting is in LIN.

v$.$ Quantum Computers can solve NP$-$complete problems in polynomial time.