Relational Algebra

Relational Algebra (RA) is a formal language which  SQL and other database softwares.

The following exercises illustrate the use of RA operators in the RA Workbench maintained by Professor Jun Yang.
A link to the workbench documentation can be found here: https://users.cs.duke.edu/~junyang/radb/

Relations used in the exercises (Link: https://lagunita.stanford.edu/c4x/DB/RA/asset/pizzadata.html )

    Person(name, age, gender)       // name is a key
    Frequents(name, pizzeria)       // [name,pizzeria] is a key
    Eats(name, pizza)               // [name,pizza] is a key
    Serves(pizzeria, pizza, price)  // [pizzeria,pizza] is a key
    
Q1 Find all pizzas eaten by at least one female over the age of 20. 

\project_{pizza} (
    (\select_{gender='female' and age >=20} Person)
    \join
    Eats)

Q5 Find the names of all people who eat at least one pizza served by Dominos but who do not frequent Dominos.

 \project_{name} (
         ((\project_{name} Frequents)
         \diff
         (\project_{name} \select_{pizzeria = 'Dominos'} Frequents)) 
    \join 
         (\select_{pizzeria='Dominos'} Serves
         \join Eats))
         
Q8 Find all pizzerias that serve only pizzas eaten by people over 30. 

\project_{pizzeria} (
         Frequents \join (
            \select_{age>30} Person)) 
            \diff \project_{pizzeria}(\project_{pizza}(\select_{age<30} Person \join Eats) 
            \diff \project_{pizza}(\select_{age>30} Person \join Eats)\join Serves)
         
Q9 Find all pizzerias that serve every pizza eaten by people over 30. 

\project_{pizzeria} Serves \diff
    \project_{pizzeria} (
            (\project_{pizza}(\select_{age>30} Person \join Eats)
                \cross
            (\project_{pizzeria} Serves))
        \diff
            (\project_{pizza, pizzeria}((\select_{age>30} Person \join Eats) \join Serves)))