A question about BCNF$.$ Consider the relation scheme $\{$pilot$,$ flight, date, time$\},$ with the following FDs: $($We use $"$to$"$ for the arrow.$)$

flight to time

pilot,date,time to flight

flight,date to pilot

Which of the following statements are correct?

After decomposing on the first FD$,$ we are done with BCNF$,$ since both obtained parts are then in BCNF$.$

If we decompose on the first FD$,$ we obtain the parts $\{$flight$,$time$\}$ with FD flight to time, and $\{$flight$,$date,pilot$\}$ with FD flight,date to pilot.

We can decompose on the third FD$,$ since its left$-$hand side is not a key.

If we decompose on the third FD$,$ we obtain the parts $\{$flight$,$date$\}$ and $\{$pilot$,$time$\}.$

We can't decompose on the second FD$,$ since its left$-$hand side is a key.