1. 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

2. 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.

3. 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:

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

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

7. 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)

9. 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

11. 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:

12. 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

13. 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.

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