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Relational Algebra
The document discusses relational algebra and its operators. It provides examples of how different relational algebra operators like projection, selection, union, intersection, set difference, cartesian product, and joins can be used to query relations. Various SQL queries are written and their equivalent relational algebra queries are shown using operators like π, σ, ∪, ∩, -, ×, and joins. The last example demonstrates using the division operator (/) to find customers that buy every product.
Relational Algebra
- 1. Relational Algebra Submitted By: WaheedImtiaz 13-arid-222 Submitted To: Munir Ahmad Dated : 04-11-2013
- 2. Relational Algebra In computerscince, relational algebra is an offshoot of first-order logic and of algebra Of sets concerned with operations over finitar relations, usually made more convenient to work with by identifying the components of a tuples by a name (called attribute) rather than by a numeric column index, which is called a relation in database terminology • Operators Select (π) Projection Where () Selection Union (∪) Setdifference (-) Cartesianproduct () Set intersection (∩) Join ( )
- 3. PROJECTION(π) Pak Id P.Name Age Address 1 M.Hafeez 30 Faisal Abad 2 Afridi 33 Karachi 3 Misbah 39 Faisal Abad 4 AbdulRazzaq 33 Lahore 5 Malik 32 Sialkot P.Id PL.Name Age Address 1 M.Hafeez 30 Faisalabad 2 Umar 26 Lahore 3 Kamran 29 Lahore 4 Abdul Razzaq 33 Lahore 5 Ahmad 24 Lahore Lions
- 4. Assuming that wewant to retrieve All records From Table Pak then: SQL Querry : Relational Algebra Querry : select * from Pak π* (Pak) Result Pak Id P.Name Age Address 1 M.Hafeez 30 Faisal Abad 2 Afridi 33 Karachi 3 Misbah 39 Faisal Abad 4 Abdul Razzaq 33 Lahore
- 5. SELECTION( ᵟ ) Pak Id P.Name Age Address 1 M.Hafeez 30 FaisalAbad 2 Afridi 33 Karachi 3 Misbah 39 Faisal Abad 4 Abdul Razzaq 33 Lahore 5 Malik 32 Sialkot P.Id PL.Name Age Address 1 M.Hafeez 30 Faisalabad 2 Umar 26 Lahore 3 Kamran 29 Lahore 4 Abdul Razzaq 33 Lahore 5 Ahmad 24 Lahore Lions
- 6. Assumin that ifwe want to retrieve data from Tables Lions of those players who belongs to Lahore then: SQL Querry : Relational Algebra Querry : Select * from Lions where Address=’Lahore’ π * ᵟAddress=’Lahore’(Lions) Result Lions P.Id PL.Name Age 2 Umar 26 3 Kamran 29 4 Abdul Razzaq 33 5 Ahmad 24
- 7. Union(U) Pak Id P.Name Age Address Category 1 M.Hafeez 30 Faisal Abad All 2 Umar 26 Lahore Bat 3 Akmal 29 Lahore WK 4 Abdul Razzaq 33 Lahore All 5 Afridi 33 Karachi All 6 Malik 32 Sialkot All 7 Misbah 39 FaisalAbad Bat Lions Id P.Name Age Address 1 M.Hafeez 30 Faisalabad 2 Umar 26 Lahore 3 Kamran 29 Lahore 4 Abdul Razzaq 33 Lahore 5 Ahmad 24 Lahore
- 8. Assuming that ifwe want to retrieve the age of players from both tables and same data retrieve only one time then: Relational Algebra Querry : SQL Querry : select Age from Pak Union select Age from Lions. Result Age 30 26 29 33 32 39 π Age (Pak) U π Age(Lions)Result
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- 10. Assuming that wewant to retrieve those city names which are exist in both columns then: SQL Query : select City from R1 intersect select City from R2 Result City California Palandari Los Angelus Relational Algebra Query : π City (R1) ∩ π City (R2)
- 11. Set difference (-) R1 201 John Corter 3241 Johansberg 202 William Philip 4543 California 203 Harry Porter 6543 Washington 204 Waqar Baig 3242 Palandari 205 RJ Asif 4312 LosAngelus Id F_Name L_Name Num City 222 Vin Diesel 5432 Los Angelus 223 Bruce Wills 6543 California 224 Jacky Chan 8765 Shinghai 204 Waqar Baig 3242 Palandari 205 RJ Sajan 4312 Los Angelus R2
- 12. Assuming that wewant retrieve Ids from Table R2 which are does not exist in table R1 then: SQL Query : select Id from R2 not exist in (select Id from R1) Result Id 222 223 224 Relational Algebra Query : π Id (R2) - π Id (R1)
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- 14. Asssuming that wewant to retrieve the all corses which are registered by all students: Relational Algebra Query : SQL Query : π* (Student*Course) Select * from student,course Result S-id Name Age Cid Title CreditHr 1 Waheed 21 705 DDS 3 1 Waheed 21 706 OS 3 1 Waheed 21 707 OOP 4 2 2 2 3 3 3 Ali Ali Ali Manan Manan Manan 24 24 24 22 22 22 705 706 707 705 706 707 DDS OS OOP DDS OS OOP 3 3 4 3 3 4
- 15. JOIN Customer Cus_id Cus_Name City Contact 101 Ali Rawalpindi 345678 102 Saleem Multan 678534 103 Waseem Islamabad 543216 104 Rizwan Rahim Yar Khan 675439 105 Ijlal Islamabad 876549 Orders Ord_id Cus_id OrderDate 35 102 27-Aug-2010 37 104 28-Aug-2010 38 105 29-Aug-2010 40 - 29-Aug-2010
- 16. Assuming that wewant to Retrieve customer and order id who’s id matches SQl Query : select customer.cus_name,orders.ord_id from customer join orders on customer.cust_id=orders.cust_id Result Cus_Name Ord_id Saleem 35 Rizwan 37 Ijlal 38 Relational Algebra Query: πcustomer.cus_name,orders.ord_id(Customer customer.cus_id=orders.cus_idOrders)
- 17. Right Join Assuming thatwe to retrieve all ids from order table and related names SQl Query : select customer.cus_name,orders.ord_id from customer Right join orders on customer.cust_id=orders.cust_id Relational Algebra Query: πcustomer.cus_name,orders.ord_id(Customer Result Cus_Name Ord_ID Saleem 35 Rizwan 37 Ijlal 38 - 40 customer.cus_id=orders.cus_idOrders)
- 18. Left Join( ) Assuming thatif we want to join two tables and retrieve the all ids and names from customer table and order ids related to customers ids then: SQl Query : select customer.cus_id,orders.ord_id from customer Left join orders on customer.cust_id=orders.cust_id Relational Algebra Query: πcustomer.cus_id,customer.cus_name,orders.ord_id(Customer Result Cus_id Cus_Name Ord_id 101 Ali 102 Saleem 103 Waseem 104 Rizwan 37 105 Ijlal 38 35 customer.cus_id=orders.cus_idOrders)
- 19. Division (/) Goal: Producethe tuples in one relation,that match all tuples in another relation. Product Pid 2 Pname H&S 3 Brite 4 Dove 5 Axe Customer CID CName 201 Waheed 202 Ali 203 Rizwan
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- 21. Suppose we wantto find the name of Customers who buy every product then: SQL Query: SELECT CName FROM Customer WHERE NOT EXISTS (SELECT Pid FROM Product WHERE Pid NOT IN (SELECT Pid from Transaction WHERE Customer.CID = Transaction.CID)) Relational Algebra Query: ∏name((transaction/product) join customer) Result CName Waheed