Relational Algebra and Relational Calculus
The first 4 minutes of this video characterize relational algebra relative to relational calculus. Relational algebra has a set of basic operations, as well as derived operations, like Join, which can be written as a composition of the basic operations. Since these operations are used frequently, they are made into a single command, the derived operation.
The last 10 minutes introduce set operations, which are used by relational calculus statements. The middle 20 minutes or so of the video work through several small examples of relational algebra. In this resource and other resources, the terms set, multi-set, and bag are used. A multi-set is simply a set that includes duplicates. A bag is just another name for a multi-set.