Download Database - DePaul University

Sets and Set Operations
A set is an unordered collection of objects called elements
Explicit definition
Implicit definition
Two sets A and B are equal if every element in A is also in
B and every element in B is also in A (A = B)
A is contained in B if every element in A is also an element
of B (A  B)
Example: Φ  A for every set A
Sets and Set Operations
The power set of A, Ρ (A) is the set of all
subsets of A
Example: Ρ (Φ) = {Φ}
The cross product of two sets
A x B = { (a, b) | a  A and b  B}
order is important: A x B  B x A in
general (x is not commutative)
A relation is a subset of A x B
cross product can be generalized
Sets and Set Operations
Set operations:
Union
A  B
Intersection
A  B
Difference
A  B
Complement (Universe of discourse) A
Venn diagram
Useful relations
| A  B | = |A| + |B| - |A  B|
DeMorgan’s law
co(A  B) = co(A)  co(B)
DeMorgan’s law can be generalized
Propositions
A proposition P is a statement that is either true or
false
Example
P : It is raining today in Chicago
Compound propositions and their truth values
P or Q (P V Q), P and Q (P Λ Q),
not P (¬P , or P), P  Q, P  Q
Propositions
DeMorgan’s laws
¬(P1 V …V Pn ) = (¬P1) Λ
… Λ (¬Pn)
¬ (P1 Λ … Λ Pn ) = (¬P1) V … V (¬Pn)
Databases
A database is a system that allows storage
and manipulation of information
A database management system (DBMS) is
a combination of hardware and software
that allows organization and manipulation
of the information
Databases
Why are databases important?
databases vs. Archiving, large size of data,
quick access and manipulation
How and why are databases used?
1. DB models aspects of the real world
2. Collection of data
• logically coherent
• Meaningful
3. Designed for specific purpose
Uses of Databases
•
•
•
•
•
Traditional (airline reservation, school, hospital, …)
Online Shopping
Search Engines
Genetic Databases
Geographical Information Systems
Sizes of Database
•
Personal (1 User), Megabytes
•
Workgroup (<25 Users), Megabytes
•
Organizational (100-1000s), Gigabytes
•
Internet (100-1000s), Terabytes
How do database represent Info.
The physical database:
a collection of files containing the data content
The schema:
a specification of the physical database’s information content and
logical structure
The database engine:
software that lets people access and modify the database contents
The data definition and manipulation languages:
SQL (Structured Query Language)
Relational database manag. Systems
(RDBMS)
RDBMS
Tables of data
Schema
• Name of table
• Names and types of attributes
Contents
• Row is a fact
• Attribute value is a characteristic
Example
Last N.
First
N.
101
102
Block
Hamilton
Jane
Cherry
103
Harrison
Kate
104
Breaux
Carroll
Customer table accountId
Logical description
(Schema)
Customer (accountId, lastName, firstName)
Table creation
statement
create table Customer (accountId integer,
lastName char(20), firstName char(20))
Client/Server Interaction
Server Computer
DBMS
Client Computer
tables
queries and updates
netw ork connection
results
disk