Relational Algebra at a Glance Operators: sets as input, new set as output Basic Set Operators union, intersection, difference, but no complement. Selection: s Projection: p Cartesian Product: X Joins (natural,equi-join, theta join, semi-join) Renaming: r

Set Operations Binary operations Result is table(set) with same attributes Watch out for naming of attributes in resulting relation. Union: all tuples in R1 or R2 Intersection: all tuples in R1 and R2 Difference: all tuples in R1 and not in R2 No complement. Why? Bags later.

Selection Produce a subset of the tuples in a relation which satisfy a given condition Unary operation… returns set with same attributes, but ‘selects’ rows Use and, or, not, >, <… to build condition Find all employees with salary more than $40,000:

Find all employees with salary more than $40,000.

Projection Unary operation, selects columns Eliminates duplicate tuples Example: project social-security number and names.

Cartesian Product Binary Operation Result is tuples combining any element of R1 with any element of R2, for R1 X R2 Schema is union of Schema(R1) & Schema(R2)

Join (Natural) Most important, expensive and exciting. Combines two relations, selecting only related tuples Equivalent to a cross product followed by selection Resulting schema has all attributes of the two relations, but one copy of join condition attributes

Other Joins and Renaming Theta join: the join involves a predicate R S Semi-join: the attributes of one relation are included in the other. Renaming:

Complex Queries Product ( pname, price, category, maker) Purchase (buyer, seller, store, product) Company (cname, stock price, country) Person( per-name, phone number, city) Find phone numbers of people who bought gizmos from Fred. Find telephony products that somebody bought

Exercises Product ( pname, price, category, maker) Purchase (buyer, seller, store, product) Company (cname, stock price, country) Person( per-name, phone number, city) Ex #1: Find people who bought telephony products. Ex #2: Find names of people who bought American products Ex #3: Find names of people who bought American products and did not buy French products Ex #4: Find names of people who bought American products and they live in Seattle. Ex #5: Find people who bought stuff from Joe or bought products from a company whose stock prices is more than $50.

Operations on Bags (and why we care) Basic operations: Projection Selection Union Intersection Set difference Cartesian product Join (natural join, theta join)