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Chapter 2 : Introduction to Relational Model

Chapter 2 : Introduction to Relational Model. Example of a Relation. attributes (or columns). tuples (or rows). Attribute Types. The set of allowed values for each attribute is called the domain of the attribute

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Chapter 2 : Introduction to Relational Model

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  1. Chapter 2: Introduction to Relational Model

  2. Example of a Relation attributes (or columns) tuples (or rows)

  3. Attribute Types • The set of allowed values for each attribute is called the domain of the attribute • Attribute values are (normally) required to be atomic; that is, indivisible • The special valuenull is a member of every domain • The null value causes complications in the definition of many operations

  4. Relation Schema and Instance • A1, A2, …, Anare attributes • R = (A1, A2, …, An ) is a relation schema Example: instructor = (ID, name, dept_name, salary) • Formally, given sets of values D1, D2, …. Dn, a relationr is a subset of D1 x D2 x … x DnThus, a relation is a set of n-tuples (a1, a2, …, an) where each ai Di • The current values (relation instance) of a relation are specified by a table. • An element tofr is a tuple, represented by a row in a table.

  5. Relations are Unordered • Order of tuples is irrelevant (tuples may be stored in an arbitrary order) • Example: instructor relation with unordered tuples

  6. Relations are Unordered • Why is the order of tuples irrelevant? • An unordered collection of elements is a set:{1, 2, 3} = {2, 1, 3}. • An ordered collection of elements is a list:(1, 2, 3)  (2, 1, 3). • A set is used to express (expressiveness). • We care you are a student, but we don’t care when you register (the order). • A list is used to process (efficiency).

  7. Schema Diagram for University Database

  8. Relational Operators

  9. Selection of tuples • Relation r • Select tuples with A=B and D > 5 • σ A=B and D > 5 (r)

  10. Selection of Columns (Attributes) • Relation r: • Select A and C • Projection • ΠA, C (r)

  11. Joining two relations – Cartesian Product • Relations r, s: • r xs:

  12. Union of two relations • Relations r, s: • r  s:

  13. Set difference of two relations • Relations r, s: • r – s:

  14. Set Intersection of two relations • Relation r, s: • r s

  15. Joining two relations – Natural Join • Let r and s be relations on schemas R and S respectively. Then, the “natural join” of relations R and S is a relation on schema R S obtained as follows: • Consider each pair of tuples tr from r and ts from s. • If tr and ts have the same value on each of the attributes in RS, add a tuple t to the result, where • t has the same value as tr on r • t has the same value as ts on s

  16. Natural Join • r s Natural Join Example • Relations r, s:

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