Requesting help in translating a SQL query to relational algebra

Question

As part of a assignment at my computer science education, I've been asked to translate a query from SQL to a relational algebra expression.

The idea here behind the query is to find all the rooms, from one single table, which has the equipment types projecter, but not a whiteboard - The following query does that, but now I'm having trouble translating it into a relation algebra expression.

SELECT 
    e.room, e.type
FROM 
    Equipment AS e
LEFT OUTER JOIN 
    Equipment AS e2 ON e.room = e2.room AND e2.type = 'whiteboard'
WHERE 
    e.type = 'projector'
    AND e2.type IS NULL;

I'd appreciate any help in translating this, as I'm quite the newbie and generally do not seem to see the logic here.

Answer 1

the logic is the following. select room, type from equipment where room has a projector. intersect with room from equipment that has a whiteboard. Keep only the part of the intersection that has a projector, but does not have a whiteboard (AND e2.type IS NULL means the room was not found in the whiteboard group)

http://sketchtoy.com/50426780

rewording:

find group A from group ROOM?EQUIPMENT that has projectors
find group B from group ROOM?EQUIPMENT that has whiteboards
Intersect A and B
keep the part of group A where room IDs are not found in group B