For each pair of statements below, please solve for whether they are logically equivalent. You must show your logical equivalence work, showing a truth table is not enough. Please include the name of each logical equivalence next to each line of your solution.

i$.,$not$(P^{{?}^{?}}$notQ${)}^{{?}^{?}}$not$(Q^{{?}^{?}}$notP$)-=$PharrQ

ii$.,P^{{?}^{?}}$not$(PQ)-=P^{{?}^{?}}$notQ

iii. $,P^{{?}^{?}}((notR$notQ$)vv(P^{{?}^{?}}R))-=(P^{{?}^{?}}(QR))vv(P^{{?}^{?}}R)$

iv$.,$not$((not(not(Pt))vvQ))-=c$