Translate the following into LTL formulas:

a$)$ Always eventually P$.$

b$)$ Always after $P$ eventually $Q.$

c$)$ If you press ctrl$-$C$,$ you will get a command line prompt. $($use atoms ctrlC and prompt$)$

d$)$ If the door is locked, it will not open until someone unlocks it$.($atoms: locked, unlocked, open$)$

e$)$ The saw will not run unless the safety guard is engaged. $($atoms: safety, running$)$