Consider the following set of relations, which describe coffee and coffee drinkers:

DRINKS $($PERSON$,$ COFFEE$)$

HAS$\_$BEAN $($COFFEE$,$ BEAN$\_$NAME$)$

BEAN $($BEAN$\_$NAME, FROM$\_$LOCATION$)$

The relation DRINKS tells us which people drink which coffees. People can drink more than one coffee. The HAS$\_$BEAN relation tells us what coffee beans go into each type of coffee. A coffee can have many beans. And the BEAN relation tells us which location each coffee bean comes from; a bean can grow in multiple relations.

$(1)$ Write RA expressions to compute each of the following. Note that you can abbreviate attribute names if you$$d like to write less $($you can use P for PERSON, C for COFFEE, BN for BEAN$\_$NAME, and FL for FROM$\_$LOCATION$).$ Each is worth $1/2$ point, except for $1($c$),$ which is worth $1$ point.

$($a$)$ Which locations grow both the beans $$Catuai$$ and "Catimor"?

$($b$)$ Which people drink a coffee that contains a bean from "Brazil" or from "Peru"?

$($c$)$ Which countries produce all of the beans in the coffee "Breakfast Delight" $($or $"$BD$")?$

$(2)$ Consider the same set of relations. Write RC expressions to compute each of the following. Again, you can abbreviate attribute names. Each is worth $1/2$ point, except for $2($c$),$ which is worth $1/2$ point.

$($a$)$ Which locations contribute a bean to a coffee consumed by $$Chris$?$

$($b$)$ Which people don't drink any of the coffees that are consumed by "Chris"?

$($c$)$ Which people drink a set of coffees that together contain all of the beans from $$Hawaii$?$