1. Session 3 Welcome: To session 3-the second learning sequence
“ Relational algebra “
Recap : In the previous learning sequences, we discussed the relational model.
Present learning: We shall explore the following topics:
- Relational algebra.
- Some operators.

2. Relational Algebra

3. Query Languages
Language in which user requests information from the database.
Categories of languages
procedural
non-procedural
“Pure” languages:
Relational Algebra
Tuple Relational Calculus
Domain Relational Calculus
Pure languages form underlying basis of query languages that people use.

4. Relational Algebra Procedural language Four basic operators
select
project
union
Intersection
The operators take one or more relations as inputs and give a new relation as a result.

5. Select Operation Notation:  p(r) p is called the selection predicate
Defined as:
p(r) = {t | t  r and p(t)}
Where p is a formula in propositional calculus consisting of terms connected by :  (and),  (or),  (not) Each term is one of:
<attribute> op <attribute> or <constant>
where op is one of: =, , >, . <. 
Example of selection:  branch-name=“Perryridge” (account)

6. Select Operation – Example
Account

7. Select Operation – Example
The result is the relation:
Account-number
Branch-name
balance
A-102
Perryridge
400 7

8. Select Operation – Example
 Balance >“700” (account)
Account-number
Branch-name
balance
A-201
Brighton
900
A-217
750 8

9. Project Operation Notation: A1, A2, …, Ak (r)
where A1, A2 are attribute names and r is a relation name.
The result is defined as the relation of k columns obtained by erasing the columns that are not listed
Duplicate rows removed from result, since relations are sets

10. Project Operation
E.g. To eliminate the branch-name attribute of account account-number, balance (account)
The result relation is:

11. Project Operation Account-number Balance A-101 500 A102 400 A-201 900
700
A-217
750
A-222
A-305
350 11

12. Union Operation Notation: r  s Defined as:
r  s = {t | t  r or t  s}
For r  s to be valid.
1. r, s must have the same arity (same number of attributes)
2. The attribute domains must be compatible (e.g., 2nd column of r deals with the same type of values as does the 2nd column of s)

13. Union Operation
E.g. to find all customers with either an account or a loan customer-name (depositor)  customer-name (borrower)
Customer-name
Account-no.
Ali
A-101
Mahmood
A-201
Ahmid
A-217
Linda
A-222
Rana
A-305
Customer-name
Loan-no.
Ali
L-11
Kasim
Ahmid
L-25
Linda
Rana
L-34
depositor
borrower

14. Union Operation Customer-name Ali Mahmood Ahmid Linda Rana ….
customer-name (depositor) customer-name (borrower)
Customer-name
Ali
Mahmood
Ahmid
Linda
Rana ….
Customer-name
Ali
Kasim
Ahmid
Linda
Rana
…..

15. Union Operation Customer-name Ali Mahmood Ahmid Linda Rana Kasim
The result relation is:
Customer-name
Ali
Mahmood
Ahmid
Linda
Rana
Kasim

16. Intersection Operation
Notation: r  s
Defined as:
r  s ={ t | t  r and t  s }
Assume:
r, s have the same arity
attributes of r and s are compatible
Note: r  s = r - (r - s)

17. Intersection Operation
E.g. to find all customers with an account and a loan customer-name (depositor)  customer-name (borrower)
Customer-name
Account-no.
Ali
A-101
Mahmood
A-201
Ahmid
A-217
Linda
A-222
Rana
A-305
Customer-name
Loan-no.
Ali
L-11
Kasim
Ahmid
L-25
Linda
Rana
L-34
depositor
borrower

18. Intersection Operation
customer-name (depositor) customer-name (borrower)
Customer-name
Ali
Mahmood
Ahmid
Linda
Rana ….
Customer-name
Ali
Kasim
Ahmid
Linda
Rana
…..

19. Intersection Operation
The result relation is:
Customer-name
Ali
Ahmid
Linda
Rana

20. Relational Algebra
Summary: In this learning sequence, we discussed Four basic operators of the topic relational algebra.

21. END