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Chapter 2: Relational Model

Chapter 2: Relational Model. Set Difference Operation – Example. Relations r , s :. A. B. A. B.   . 1 2 1.  . 2 3. s. r. r – s :. A. B.  . 1 1. Set Difference Operation. Notation r – s Defined as: r – s = { t | t  r and t  s }

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Chapter 2: Relational Model

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  1. Chapter 2: Relational Model

  2. Set Difference Operation – Example • Relations r, s: A B A B    1 2 1   2 3 s r • r – s: A B   1 1

  3. Set Difference Operation • Notation r – s • Defined as: r – s = {t | t rand t  s} • Set differences must be taken between compatible relations. • r and s must have the same arity • attribute domains of r and s must be compatible

  4. Example Find the names of all customers who have an account but no loan from the bank. customer_name (depositor) - customer_name (borrower) Depositor Borrower

  5. Cartesian-Product Operation – Example • Relations r, s: A B C D E   1 2     10 10 20 10 a a b b r s • r xs: A B C D E         1 1 1 1 2 2 2 2         10 10 20 10 10 10 20 10 a a b b a a b b

  6. Cartesian-Product Operation • Notation r x s • Defined as: r x s = {t q | t  r and q  s} • Assume that attributes of r(R) and s(S) are disjoint. (That is, R  S = ). • If attributes of r(R) and s(S) are not disjoint, then renaming must be used.

  7. Composition of Operations • Can build expressions using multiple operations • Example: A=C(r x s) • r x s • A=C(r x s) A B C D E         1 1 1 1 2 2 2 2         10 10 20 10 10 10 20 10 a a b b a a b b A B C D E       10 10 20 a a b 1 2 2

  8. Banking Example branch (branch_name, branch_city, assets) customer (customer_name, customer_street, customer_city) account (account_number, branch_name, balance) loan (loan_number, branch_name, amount) depositor (customer_name, account_number) borrower(customer_name, loan_number)

  9. Example • Find the names of all customers who have a loan at the Mirpurbranch. customer_name (branch_name=“Mirpur” (borrower.loan_number = loan.loan_number(borrower x loan))) • Find the names of all customers who have a loan at the Mirpurbranch but do not have an account at any branch of the bank. customer_name (branch_name = “Mirpur” (borrower.loan_number = loan.loan_number(borrower x loan))) – customer_name(depositor)

  10. Examples • Find out the customer names who live in Khulna city customer_name (customer_city=“khulna”(customer)) • Find out the customer names who have an account but do not have a loan at any branch of the bank. customer_name (depositor) – customer_name(borrower)

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