Suppose the relation R$1($A$,$B$)$ and R$2($B$,$C$,$D$)$ have the following tuples:

Compute the theta$-$join of R$1$ and R$2$ with conditions R$1.$B $=$ R$2.$B AND R$1.$A $<$ R$2.$C$.$ Which of the following tuples is

in the result? Assume each tuple has schema $($A$,$ R$1.$B$,$ R$2.$B$,$ C$,$ D$).$

a$)(2,$ G$,$ T$,8,9)$ b$)(4,$ C$,$ C$,7,8)$ c$)(4,$ C$,$ C$,5,6)$ d$)(1,$ A$,$ C$,4,3)$

Questions $(7,8,9,$ and $10).$ Give the following queries in the relational algebra using the relational schema:

student$($id$,$ name$)($can be called ST$)$

enrolledIn$($id$,$ code$)($can be called EN$)$

subject$($code$,$ lecturer$)($can be called either SU$1$ or SU$2)$

Who teaches cs$1500$ or cs$3020?$

Who teaches at least two different subjects?

What are the names of students in cs$1500$ or cs$3010?$

What are the names of students in both cs$1500$ and cs$1200?$

Bonus question. Consider the database with the following schema:

Person$($name$,$ age, gender$)$ name is key

Frequents$($name$,$ iceCreamShop$)($name$,$ iceCreamShop$)$ is a key

Eats$($name$,$ flavor$)($name$,$ flavor$)$ is a key

Sells$($iceCreamShop$,$ flavor, price$)($iceCreamShop$,$ flavor$)$ is a key

Find an ice cream shop that is frequented by people older than $30$ but younger than $40$ years old.

A B

$1$ A

$7$ T

$2$ G

$4$ C

$9$ T

B C D

C $56$

A $78$

T $89$