abordagem er - dca.ufrn.branderson/ftp/dca0120/aula2.pdf · técnica de modelagem de dados mais...

84
Abordagem ER Capítulo 2

Upload: hoangdung

Post on 26-Jan-2019

212 views

Category:

Documents


0 download

TRANSCRIPT

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

$

Abordagem ER

Capítulo 2

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

Abordagem Entidade-Relacionamento

� Técnica para construir modelos conceituais de bases de dados

� Técnica de modelagem de dados mais difundida e utilizada

� Criada em 1976, por Peter Chen

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

Abordagem Entidade-Relacionamento

� Padrão de fato para modelagem conceitual

� Não é única:

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� Técnicas de modelagem orientada a objeto (UML) baseiam-se nos conceitos da abordagem ER

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

Abordagem Entidade-Relacionamento

� Modelo de dados é representado através de um

� � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � �

� Modelo ER é representado graficamente

� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � �

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

Conceitos centrais da abordagem ER

� Entidade� Relacionamento� Atributo

� Generalização/especialização� Entidade associativa

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

Entidade

Conjunto de objetos da realidade modelada sobre os quais deseja-se manter informações no banco de

dados

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

Entidade – exemplos

� Sistema de informações industrial

� � � � � � � �

� � � � � � � � � � � � � �

� � � � � �

� � � � � � � �

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

Entidade – exemplos

� Sistema de contas correntes

� � � � � � �

� � � � � � � � � � � �

� � � � � � � �

� � � � � � � �

� Entidade pode representar

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

� �

� � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � ��

� � � � � � � � � �

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

� � � � � � � � � � � � � � � �

Entidade no DER

� Representada através de um retângulo� Retângulo contém o nome da entidade.

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

$ �

Entidade e instância

� Para referir um objeto particular

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

$ $

Entidade e instância - terminologia

conjunto elemento do conjuntoentidade instância

classe instânciaconjuntode entidades entidade

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

$ �

Propriedades de entidades

� Entidade isoladamente não informa nada� É necessário atribuir propriedades às entidades

� Propriedades especificadas na forma de

� � � � � � � � � � � � �

� � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

$ �

ExercícioIdentificar entidades

Sistema de vendasDeseja-se construir um banco de dados para um sistema de vendas. Em cada venda são vendidos vários produtos e um determinado produto pode aparecer em diferentes vendas. Cada venda é efetuada por um vendedor para um determinado cliente. Um produto está armazenado um uma prateleira.

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

$ �

Exercício 3.5Identificar entidades

� � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

! � � � � � � � � � � � � � � � � � � � � � � � � � ! " ! # � �$

% � � � � � � � & � � � � � � � � " � � � � � � � � � � � � � � � � � � � � � � � � � ! � � � ! � � �

� � " ! � � � � � � � ' � � � � � ( � � )

* � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ' � � � � � � � + � � ! � � � � � � �

� � � � � � � � � � � �$

* , � � � ! � � � � � � � � � � � � � � � � � # � � + � � + � � � � � � � � � ! � � � ! � � � �

+ � � � � � �$

% � � + � � � � � + � � � + � � � ! � � � � & � � � � � ! � � � � � � �$

, � � � ! � � � � � � + � � � � � � � � � � ! " � � � + � � � � � � - . � � � ! � � + � � � � �$

% � � + � � � � � + � � � � � ! " � � � � & � � � � � ! � � � � � � �$

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

$ %

Exercício 3.5Entidades identificadas

� ADMINISTRADORA� CONDOMÍNIO� UNIDADE� PESSOA

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

$ �

Relacionamento - conceito

Conjunto de associações entre entidades sobre as quais deseja-se manter informações na base

de dados

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

$ �

Relacionamento no DER

� � � � � � � � � � � � � � � � � � � � �

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

$ �

Relacionamento e instância

� Relacionamento é um conjunto de associações entre instâncias de entidades� Uma instância (ocorrência) é uma associação

específica entre determinadas instâncias de entidade� Exemplo (relacionamento LOTAÇÃO)

� � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # $ %

Diagrama de ocorrências

& '

& (

& )& *& +

& ,& -

& .

& '/

0 ' & ./

0 ' & ,/

0 .

& */

0 -

0 ' 0 -0 .

1 2 3 4 5 6 5 1

7 8 9 : 7 ; < = >

? 1 @ 6 A 4 B 2 6 C 1 2 3 B

D > E < F G >

1 2 3 4 5 6 5 1

= 7 9 < : E < 8 7 H E >

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # � �

Auto-relacionamento

PESSOA

CASAMENTOmarido esposa

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # � $

Papel de relacionamento

� Função que uma ocorrência de uma entidade cumpre em uma ocorrência de um relacionamento� Relacionamento de casamento

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � �

� Relacionamentos entre entidades diferentes:

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # � �

Auto-relacionamentodiagrama de ocorrências

� �

� �

� �

� �

� �

� �

� �

� �

� �

� �

� �

� �

C 6 ? 4 5 B

1 � B 6

C 6 ? 4 5 B

1 � B 6

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # � �

ExercícioIdentificar relacionamentos

Deseja-se construir um banco de dados para um sistema de vendas. Em cada venda são vendidos vários produtos e um determinado produto pode aparecer em diferentes vendas. Cada venda é efetuada por um vendedor para um determinado cliente. Um produto está armazenado um uma prateleira.

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # � �

Cardinalidade de relacionamentos

� Propriedade importante de um relacionamento

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� Chamada de cardinalidade de uma entidade em um relacionamento� duas cardinalidades

� � � � � � �

� � � � � �

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # � �

Cardinalidade máxima no DER

D > E < F G >= 7 9 < : E < 8 7 H E > 7 8 9 : 7 ; < = >

��

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # � �

Cardinalidade máxima - DER

D > E < F G >= 7 9 < : E < 8 7 H E > 7 8 9 : 7 ; < = >

��

� � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � ! � � � � � � � � � � � � � � � " � � � # " �

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # $ %

Cardinalidade máxima no DER

& ' ( ) & * * + , - & + - . + / 0 / ) ) 1 2 0 3 + 4 &

5 6 7 8 9 : 8 ; 6 < : = > & 2 ? 3 4 + 4 & + / @ + 4 /

/ ( / * ? / 4 + + 2 / ? + A B / C ( / 4 & . & * ? + )

+ * * / 0 3 + 4 + * . - 3 ? + * > D 2 E C / 0 / ) ) 1 2 0 3 + * 4 &

6 ; 7 9 6 F 8 5 =

G = : 8 H I =5 6 7 8 9 : 8 ; 6 < : = 6 ; 7 9 6 F 8 5 =

JK

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # $ �

Cardinalidade máxima - valores

� Para projeto de BD relacional

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � �

� Dois valores de cardinalidades máximas são usados

� � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � ��

� � � � � � � � � � � � � �

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # $ �

Classificação de relacionamentos

� Cardinalidade máxima pode ser usada para classificar relacionamentos binários� Relacionamento binário

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � �

� Relacionamentos binários

� � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � �

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # � �

Relacionamentos 1:1

7 6 � � = 8

� 8 � 8 ; 6 < : =

� � � �

6 ; 7 9 6 F 8 5 =

8 G = � 8 H I =

; 6 � 8

� � � � �

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # � �

Relacionamentos 1:n

8 G � < = � < � � 9 � H I = � � 9 � =

�2

6 ; 7 9 6 F 8 5 = 5 6 7 6 < 5 6 < : 6

� 2

6 ; 7 9 6 F 8 5 =

� � 7 6 9 � � � I =

� 2

* - ( & ) � 3 * / ) * - ( & ) � 3 * 3 / 2 + 4 /

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # � $

Relacionamentos n:n

� � � � � � � � � � � � � � � � � � � � �

� �

� � � � � � � � � � � � � � � � � � �

� �

� � � � � � � � � � � � � � � � � � � � �

� �

� � � � �

! " # $ " % & ' ( "

� �

) * + , * - . * ) * + , * � / � . /

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

$ $

ExercícioIdentificar cardinalidades

Deseja-se construir um banco de dados para um sistema de vendas. Em cada venda são vendidos vários produtos e um determinado produto pode aparecer em diferentes vendas. Cada venda é efetuada por um vendedor para um determinado cliente. Um produto está armazenado um uma prateleira.

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

$ �

Exercício 3.6Identificar relacionamentos

� � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

! " � � � � � � � � � � � � � � � � � � � � � � � � � " # " $ � �%

& � � � � � � � ' � � � � � � � � # � � � � � � � � � � � � � � � � � � � � � � � � � " � � � " � � �

� � # " � � � � � � � ( � � � � � ) � � *

+ � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ( � � � � � � � , � � " � � � � � � �

� � � � � � � � � � � �%

+ - � � � " � � � � � � � � � � � � � � � � � $ � � , � � , � � � � � � � � � " � � � " � � � �

, � � � � � �%

& � � , � � � � � , � � � , � � � " � � � � ' � � � � � " � � � � � � �%

- � � � " � � � � � � , � � � � � � � � � � " # � � � , � � � � � � . / � � � " � � , � � � � �%

& � � , � � � � � , � � � � � " # � � � � ' � � � � � " � � � � � � �%

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

$ �

Exercício 3.6Identificar relacionamentos

� � � � � � � � � � � �

� � � � � �

� � � � � �

� � � � �

��

� � � � � � � � � �

� � � � � � � � � � � � � � � � � �

��

��

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

$ �

Relacionamento ternário

� � � � � � � � � �� � � � � �

� � � �

� � � � � � � � � � �

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

$ �

Cardinalidade em relacionamento ternário

� � � � � � � � � �� � � � � �

� � � �

� � � � � � � � � � �

� � � � � � � � � � � � � �

� � � � � � � � � � � �

� � � � � �

� � � � � � �

� � � � � � �

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

$ �

ExercícioRelacionamento ternário

Identifique as entidades, os relacionamentos e as respectivas cardinalidades para o seguinte problema:Em uma empresa de desenvolvimento de sistemas informatizados, pessoas são alocadas a tarefas. No momento da alocação da pessoa a tarefa, também lhe é alocado um equipamento para resolver a tarefa.

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

$ �

Exercício 2.7Mostre como o modelo ER da ao lado pode ser representado sem uso de relacionamentos ternários, apenas usando relacionamentos binários

� � � � � � � � � �� � � � � �

� � � �

� � � � � � � � � � �

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

� �

Exercício 2.7(solução)

� � � � � � � � � �� � � � � �

� � � �

�� � � � � � � � � �

� ��

� � � ��

� �

� ��

� �

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

� �

Exercício 2.7(solução incorreta)

� � � � � � � � � � � � � � � �

� � � � � � �

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # $ %

Cardinalidade mínima

� Número mínimo de ocorrências de entidade que são associadas a uma ocorrência de uma entidade através de um relacionamento� Para fins de projeto de BD, consideram-se apenas

duas cardinalidades mínimas

& ' ( ) * + ( , + * ( * - . / + . ( 0

& ' ( ) * + ( , + * ( * - . / + . ( 1

� Denominação alternativa:

& ' ( ) * + ( , + * ( * - . / + . ( 1 2 3 ( 4 4 & ' + ( 5 6 & & 7 ) + 8 ( 9 : ) + ( ;

& ' ( ) * + ( , + * ( * - . / + . ( 0 2 3 ( 4 4 & ' + ( 5 6 & & < ' + & ( , ;

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # $ �

Cardinalidade mínima - DER

� � � � � � � � �

� � � � � �

��

��

� ��

� �

� ��

� �� � � �

��

� �

� � � �� �

� �

� � � �

��

� �

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # $ $

Exemplo - entidades e relacionamentos

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� ��

� � � ��

� �

� � � � � � � � � � � � � � � �

� ��

� �� ��

� �

� ��

� �

� ��

� �

� � � � � � � �

� � �� � � � �

� ��

� � � ��

� �

� � � � � � � �� � � � � �

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # $ �

Exercício 2.15

� Modifique as cardinalidades mínimas de forma a especificar o seguinte:

& � . ' � ) 4 & 6 & < & * - - 4 9 ( ) � ( � + &�

+ 4 9 & ��

* - � - < & 4 4 � + )

( & . - & 4 � . ( * + 4 ' + < , + ( - . 4 - � ' � ) ) / ' � , &

& � . ( , � &�

. - 4 . & � � - 6 & + 4 ' ) + 9 & - . - � � .

' � ) 4 &�

* - � - < - ) . ( - ' - ) < & ) ( , 8 � . 9 - . < & & 7 ( ' &

* - * ( * & 4

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # $ �

� � � � � � �� � � �

� � � � � �

� � �

Atributo

Dado ou informação que é associado a cada ocorrência de uma entidade ou de um relacionamento

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # $ �

ExercícioIdentificar atributos

� � � � � � � � � � � � � � � � � � � � � � � ��

� � �� � � � � � � � � �� � � �� � ��

� � � � � � � � � � �

� �

� � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � ��

� � � � � �

� �

� � � � � � � ��

� � � � ��

� � � � � � �� ��

� ��

� � � � � �

�� � � � � � �

� � � � � �

� � � � � � � � � � � � � ��

� � � � � � � � � � � � � � � � � � � � � ��

� � � � � �

� �

� � � � � � � � � � � � � � � � �� � � � � � � � ��

� � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � �� � � � � � � ��

� � � � � � � � � � � � �� ��

� � � � � � � � � � � � � � � � � � � � � ��

� � � � � � � � �

� � � � � � � � � � � � � � ��

� � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � ��

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # $ �

Atributos com cardinalidade

� Cardinalidade mínima

& ( 9 ) + 7 � 9 & & 7 ) + 8 ( 9 : ) + & � ' ( ) * + ( , + * ( * - . / + . ( 3 1 ; �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

& ( 9 ) + 7 � 9 & & < ' + & ( , � ' ( ) * + ( , + * ( * - . / + . ( 3 0 ; �

� Cardinalidade máxima

& ( 9 ) + 7 � 9 & . & & � ( , & ) ( * & � ' ( ) * + ( , + * ( * - . � � + . ( 3 1 ; �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

& ( 9 ) + 7 � 9 & . � , 9 + � ( , & ) ( * & � ' ( ) * + ( , + * ( * - . � � + . ( 3 ; �

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # $ �

Atributo com cardinalidade

� � � � � � � � � � � � � � � � �

� � � � �

� � � � � � � � � � � � � � �

� � � � � � � � � � � � �

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # � �

Exercício 2.16

Sem usar

& ( 9 ) + 7 � 9 & 4 & < ' + & ( + 4�

- .

& ( 9 ) + 7 � 9 & 4 . � , 9 + � ( , & ) ( * & 4

construa um DER que contenha as mesmas informações do modelo anterior

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # � �

Atributo em relacionamento

� � � � � � � � � � � � � � � � � � � � �

� � � � � �

� � � � � � � � � � � � � �� � � � � � � � � � �

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # $ %

Atributo em relacionamento 1:n

& ' ( ) ( � * ' + ) , - . / . 0 - / 1 2 . 3 4 5 * ( 6 )

7 89

: ;

< = > = ? @ A � B � C

7 89

D ;

E ? @ F = B G @ H = C

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # $ �

ExercícioAtributos

Altere o modelo ER do sistema de vendas para incorporar as seguintes informações:Tanto clientes, quanto vendedores podem ter vários telefones.Um produto pode ter vários preços, cada um com uma data de início e de fim de validade.Para cada produto vendido em uma venda, é necessário conhecer o número de unidades vendidas e o preço de venda.

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # $ �

Identificador de entidade

� Cada entidade deve possuir um identificador

Identificador de entidade=

conjunto propriedades de uma entidade (atributos e relacionamentos) cujos valores servem para

distinguir uma ocorrência da entidade das demais ocorrências da mesma entidade

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # $ $

Atributo identificador

� * � � � )

� D � � � � � �

� � � � � �

D � � �

� + ) � * * ' + )

D � � � � � � � � � � � � � � �

� � � � � � � � � �

D � � � � � � � � � � � � � �

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # $ �

Relacionamento identificador

� Entidade fraca

* � � + * � ) 6 � 6 * � * ( 6 * ( � *

7 :9

: ; 7 89

D ;

D � � �� � � � � D � � �� � � � � �

D � � � �

D � � �

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # $ �

Relacionamento identificador (recursão)

7 :9

: ;

7 89

D ;� + � � � � � � � � �

D � � � � � �

� � � � � � �

& ' ' )

7 :9

: ;

7 89

D ;

D � � � � � �

� � � � � �

* � � + * � )

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # $ �

Identificador de relacionamento

� Uma ocorrência de relacionamento diferencia-se das demais do mesmo relacionamento pelas ocorrências de entidades que dela participam.

* ( � * ( � * ' + � ) � � ) � � � � + � � * � �

D D

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # $ �

Relacionamento com atributo identificador

� � 6 ' � � � � ( � � � ) � ) � ' * ( � *

D D

� � � � � � � �

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # � �

ExercícioIdentificador de entidade

Determine quais os identificadores das entidades do sistema de vendas

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # � �

& � D � � �

Exercício 2.11

Construa um DER que modela a mesma realidade que a mostrada no DER abaixo, usando apenas relacionamentos 1:n.

* ( � * ( � * ' + � ) � � ) � � � � + � � * � �

7 :9

D ; 7 89

D ;

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # � %

Exercício 2.11(solução)

* ( � * ( � * ' + � � + � � * � �

7 89

D ; 7 :9

D ;

� � � � � � ( � � � � � � � �& � D � � � � � � � � �

) � � ) � � �

7 :9

: ; 7 :9

: ;

* ( � * ( � * ' + � ) � � ) � � � � + � � * � �

7 :9

D ; 7 89

D ;

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # � �

Generalização/especialização

� Conceito permite

� � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � �

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # � �

Generalização/especialização

� ' * ( � *

� * � � � )

& � � ' � )

� * � � � )

� � + � 6 ' � )

D � � �

� � � � � �

� ' � � � �

& ' ' )

7 :9

: ; 7 89

D ;

� � � � � � � � �

� � � � D � � � � � �

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # � $

Generalização/especialização

� Herança de propriedades

� Herdar propriedades significa

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �9

� � � � � � � � � � � � � � � � � � � � � � � � � � � � D � � � � � � D � � � � �

� � D � � � � � � � � � � � � � D � � D �

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # � �

Especialização total

� ' * ( � *

� * � � � )

& � � ' � )

� * � � � )

� � + � 6 ' � )

<

� D � � � � � � � � � �

� ' * ( � * � � �

� * � � � ) & � � ' � ) � �

� * � � � ) � � + � 6 ' � )

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # � �

Especialização parcial

& � ( � ' � ( � + ' �

� � � � + ' � � ) � * � + * � � + ' )

F

� D � � � � � � � D � � � � �

& � ( � ' � ( � + ' � �

� � � � + ' � � ) � �

� * � + * � � + ' )

� � � � �

� � D � � � D � � � �

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # � �

Generalização/especialização (recursão)

5 * � � � �

) � � � � � 5 * � � � � � � � � � � � � � ) + � �

5 * � � � �

� * + + * � � + *

5 * � � � �

) � � � ' � �

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # � �

Especialização não exclusiva (compartilhada)

� * � � � )

� + � & * � � � + & � ( � ' � ( � + ' � ) � ( �

� � � � D � � D � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � �

� � � � � � � � �

� � � � � � � � � � � � � � ��

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # � �

Tipos de generalizações/especializações

� �� �� � � � � � � � � � � � �

� �� �� � � � � � � � � � �

� � � � � � � � �� � � � � � �

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

$ %

Exercício

Verifique se é possível utilizar com vantagem o conceito de generalização/especialização no exemplo do sistema de vendas

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

$ �

Exercício 2.12

� � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � �

� � � � � � � � � � � � � � � � ��

� ��

� � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

� � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � �

� ��

� � � ��

� �

� � � �� � � � � � � �� � � � � � �

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

$ �

Exercício 2.12

� � � � � � � � � � � � � � � � �

� ��

� � � ��

� �

� � � �

� � � � � � � �

� � � � � � � � �� � � �

� � ��

� � � ��

� � ��

� � ��

� ��

� �

� ��

� �

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

$ �

Entidade associativa

� Modificar modelo:� Adicionar medicamentos prescritos em uma

consulta

� � � � � � � � � � � � � � � � � � � �

� �

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

$ �

Substituindo relacionamento por entidade

� � � � � � � � � � �

� � � � � � � �

� � � � � � � �

� ��

� �

� �

� ��

� �

��

� � � � � �

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

$ �

Entidade associativa

� � � � � � � � � � � � � � � � � � � �

� �

� � � � � � � � � �

� � � � � � � � � �

��

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

$ $

SímbolosDER

� � � � � � � � � � � � �

� � � � � �

� � � � � � � � � � � � �

� � � � � � �

� � � � � � �

� � � � � � � � � �

� � � � � � � � � � � � �

� � � � � � � � � �

� � � � � � � � � � � � �

� � � � � � � � � � � �

� � � � � �

� � � � � � � �

! %"

% #

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

$ �

DER de uma farmácia

� � � � � � �

� � � � � � �

� � �

� � � � � � � �

� � � � � � � � � � � � � � � �

� � � �

� � � �

� � � � �

� ��

� �� ��

� �

� ��

� �

� ��

� �

� ��

� �� ��

� �

� ��

� �

� ��

� �

� ��

� �

� ��

� �

� ��

� �

� ��

� �

� ��

� �

� ��

� �

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

$ �

DER recursos humanos

� � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � �

� � � � � � � �

� � � � �

� � � � � �

� � � � � � � � � � � � � � � � � �

� � � � � � �

� � � � �

� � � � � � � � �

� � � �

� � �

� � �

� ��

� �� ��

� �

� ��

� �

� ��

� � � ��

� �

� ��

� �

� � � � � �

� ��

� �

� ��

� �

� � � � �� � ��

� � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � ��

� � ��

� �� � �� � � � �� � � � �� ��

� ��

� � � � � � � � � � ���

�� � �� � � � � �

! " " #

� �Exercício 3.6

Identificar entidades, relacionamentos e atributos

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

� � � � � � �

� � � ��

� � � � � � � � � � � � � � � � � � � � � � � � � ��

� � � � � � � � � � � � � � � � � ��

� � � � � � � � � � ��

� � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � ��

� � � ��

� � � � � � �� �

��

� � �

� � � � � � � � � � � � � � � � � � � � � � � � ��

� � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � ��

� � � � � � � � � � � � � � � � � � � � � � � � � � ��

� � � � � � � � � � � � � � � � � � � � � ��

� � � � � � � � � � � � � � � �

� � � � � � � � � � � � � ��

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � ��

� � � � � ��

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � ��

� � � � � � � � � � � � � � � � � � � ��

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

� � � � � � � � � � � � � � � � � � ��

� � � �

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # $ %Exercício 3.6 (continuação)

Identificar entidades, relacionamentos e atributos

& ' ( ) * + ( , * - ( . . / 0 1 / 0 2 ( . ) ' 0 3 4 2 3 . ) * + * . 2 , * + ( .5

6 ( 1 3 4 2 3 ) ' 0 3 4 2 3 .

) * + * . 2 , * + ( . - ( + 3 1 * ' / 7 * , 8 0 2 * .5

9 * , * ) * + * ) ' 0 3 4 2 3 : 4 3 ) 3 . . ; , 0 (

. * < 3 , . 3 / - , := 4 ( 1 3 3 . 3 / . ( < , 3 4 ( 1 3>

. 3 / 2 3 ' 3 8 ( 4 3 3 . 3 / 3 4 + 3 , 3 ? (5

& ' : 1 + 0 . . (>

) * + * ) ' 0 3 4 2 3 , 3 ) 3 < 3 / 1 4 @ 1 3 , ( + 3 * . . ( ) 0 * + (5

A 0 4 * ' 1 3 4 2 3>

+ 3 . 3 B * 1 ( . . * < 3 , C / 3 8 0 2 * . ) * + * ) ' 0 3 4 2 3 2 3 1

3 1 - , 3 . 2 * + * .5

D 1 ) ' 0 3 4 2 3 - ( + 3 2 3 , E ; , 0 * . 8 0 2 * . 3 1 / 1 0 4 . 2 * 4 2 3 4 (

2 3 1 - (5

F G ( . G ( 1 * 4 2 0 + ( . , 3 7 0 . 2 , ( . H 0 . 2 I , 0 ) ( . + 3 * ' / 7 / : 0 .5

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # $ �

Exercício 3.6Identificar entidades

� LOCADORA� FILME� FITA� CLIENTE� CATEGORIA (será que é atributo?)� ATOR� empréstimo é entidade ou relacionamento?

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # $ �

Exercício 3.6relacionamentos

� � � � � �

� � � � � � � �

� � � �

� �

� �

� � � �� �

� � � � � � � �

� � � �

� � � � �

� � � � � � � � !

��

� � " #

$ � � � % " # � �

� � � � � & '

$ � � � ( � �

� � � � � � �

� �

� " $ � ) " # �

$ % $ � �

� * � � � +

� �

� � � � � � ,

� * � � � � � � - � �

� �

� � � � �� � �� � � �

� � � � � � � � � � � � � � � � � �� �� � � � �� �� � � � �� � �� � � �� � �� � �� � � � �� � � � �� � � � � � � � � � � � � � � � �� � �� � �� � � � � � ! " " # $ �

Exercício 3.6Atributos e identificadores

� �

� �

� � � � � �

� � � � � � � �

� � � �

� �

� �

� � � �� �

� � � � � � � �

� � � �

� � � � �

� ��

� �

� ��

� �

� � � � � � � � !

� ��

� �� ��

� �

� ��

� �

� � " #

$ � � � % " # � �

� � � � � & '

$ � � � ( � �

� ��

� �

� ��

� �

� ��

� �

� � � � � � �

� �

� " $ � ) " # �

$ % $ � �

� * � � � +

� �

� � � � � � ,

� * � � � � � � - � �

� �