$3.(15$ points$)$ Consider the following application:

We want to model basketball teams $($B$).$

$$ Each team has a hometown $($T$).($But each hometown can have multiple teams$)$

$$ Each team has a set of players $($P$).$

$$ Every year $($Y$),$ a player is on one and only one basketball team. $($But he can change team

the next year$)$

$$ Every year, a player can have one manager $($M$).($But he can change manager the next

year$)$

$$ Every year, a manager only deals with teams from a certain hometown $($but that can

change next year$).$

Suppose we want to use a single table to store all these information $($BMPTY$)$

a$.$ Write down all functional dependencies. $($For example, for the first bullet point: B $$T$).$

Notice that not all bullet points have functional dependencies.

b$.$ Find ALL candidate keys

c$.$ Is the relation in Boyce$-$Codd normal form? Why $($not$)?$

d$.$ Is the relation in $3$ rd normal form? Why $($not$)$