Relational algebra - How to get all cards not used in a purchase?

Question

Suppose you have two tables:

Purchase(cardID,itemID)

MembershipCard(cardID,clientID,companyName)

How can I get all cardID's which were not used in a purchase using relational algebra?

It seems like division to me but I'm not sure

Answer 1

You have to take all MembershipCards and remove all the ones that are in Purchase:

π_cardID(MembershipCard) - π_cardID(Purchase)