Questions and Answers
Relational algebra is made up of which of the following five fundamental operations?
Which of the following should you use to ensure that union-compatibility exists between two relations from which you want to create a third relation that does not contain duplicate information?
Which of the following SQL statements should you use to restrict a Cartesian product relational algebraic operation to avoid the redundancy of creating a relation that contains every possible row combination from two relations?
What is the term for a binary operation that combines two relations where the combination of rows satisfies a predicate?
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Consider the following relational algebraic expression: σ location = 'BldgA' (Employee). Which SQL expression is equivalent to this relational algebraic expression?
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To which of the following is a join operation equivalent?
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What do the relations known as that require the two relations involved to have the same number of attributes with matching domains?
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What function does the intersection relational algebraic operation perform?
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Consider the following SQL statement: SELECT Proj_Mgr., Contractor. FROM Proj_Mgr, Contractor WHERE Proj_Mgr.e_id = Contractor.e_id. What type of operation is represented by the SQL statement?
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Selection is a unary operation that:
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What function does the union relational algebraic operation perform?
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Projection is a unary operation that:
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Which relational algebraic operation creates a new relation containing every possible pair of rows from the two original relations?
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Consider the following relational algebraic expression: Employee ∪ Proj_Mgr. Which SQL statement is equivalent?
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You have two relations from which you can extract data: Employee and Proj_Mgr. Which relational algebraic operation should you use to determine which employees are not project managers?
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You have two relations from which you can extract data: Proj_Mgr and Contractor. Which relational algebraic operation should you use to determine the project managers who are contractors?
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Which relational algebraic operation is represented by the symbol π?
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Consider the following SQL statement: SELECT Customer.c_id, last_name, first_name, address, city, state, zip, Tour.c_id, tour_no FROM Customer, Tour WHERE Customer.c_id = Tour.c_id. What type of operation is represented by this SQL statement?
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Consider the SQL statement: SELECT * FROM Employee WHERE hire_date = '06-01-2004'; Which relational algebraic expression is equivalent?
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What distinguishes an equi-join from a theta-join?
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Consider the following relational algebraic expression: Employee X Project. Which SQL statement is equivalent to this relational algebraic expression?
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Which symbol indicates a Cartesian product relational algebraic operation?
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Study Notes
Fundamental Operations of Relational Algebra
- Relational algebra consists of five primary operations: selection, projection, Cartesian product, union, and difference.
Ensuring Union-Compatibility
- To create a third relation without duplicates from two relations, utilize the projection operation.
Restricting Cartesian Products in SQL
- The WHERE clause is essential to limit Cartesian products and reduce redundancy by restricting row combinations.
Theta-Join Definition
- A theta-join is a binary operation that combines two relations based on a predicate satisfied by the rows.
Equivalent SQL Expressions for Selection
- The expression σ location = 'BldgA' (Employee) corresponds to SQL: SELECT * FROM Employee WHERE location = 'BldgA';.
Equivalence of Join Operations
- A join operation is equivalent to a restricted Cartesian product, combining rows based on specific conditions.
Union-Compatible Relations
- Relations that must have the same number of attributes with matching domains are known as union-compatible relations.
Function of Intersection Operation
- The intersection operation yields a new relation containing rows common to both input relations.
SQL Representation of Intersection
- The SQL statement SELECT Proj_Mgr., Contractor. FROM Proj_Mgr, Contractor WHERE Proj_Mgr.e_id = Contractor.e_id represents an intersection of two relations.
Selection Operation Characteristics
- Selection is a unary operation that selects rows from a single relation based on a specified condition.
Function of Union Operation
- The union operation merges rows from two relations into one, ensuring the elimination of duplicate rows.
Characteristics of Projection Operation
- Projection is a unary operation that chooses specific columns from a single relation to produce a new relation.
Cartesian Product Definition
- The Cartesian product is a binary operation generating a new relation with every possible pair of rows from two relations.
Equivalent SQL for Union
- The expression Employee ∪ Proj_Mgr corresponds to SQL: SELECT * FROM Employee UNION SELECT * FROM Proj_Mgr;.
Identifying Non-Project Managers
- To find employees who are not project managers, employ the difference operation.
Finding Common Project Managers
- The intersection operation is used to identify project managers who are also contractors.
Projection Symbol
- In relational algebra, projection is denoted using the symbol π.
SQL Representation of Equi-Join
- The SQL statement SELECT Customer.c_id, last_name, first_name, address, city, state, zip, Tour.c_id, tour_no FROM Customer, Tour WHERE Customer.c_id = Tour.c_id represents an equi-join operation.
Equivalent Expression for Specific SQL Queries
- The SQL statement SELECT * FROM Employee WHERE hire_date = '06-01-2004' is equivalent to the relational algebra expression σ hire_date = '06-01-2004'(Employee).
Distinction Between Equi-Join and Theta-Join
- An equi-join uses only the equality operator in its predicate, while a theta-join can utilize any comparison operator.
SQL Equivalent for Cartesian Products
- The expression Employee X Project corresponds to SQL: SELECT Employee., Project. FROM Employee, Project.
Symbol for Cartesian Product
- In relational algebra, the symbol X signifies the operation of Cartesian product.
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