Relational Algebra & Calculus

Q1. The selection operation in relational algebra:

1. A.Selects tuples (rows) that satisfy a condition✓ Correct
2. B.Selects specific columns from a given relation
3. C.Renames a relation or its attribute identifiers
4. D.Combines two relations into a single relation

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Q2. The projection operation in relational algebra:

1. A.Deletes tuples from a stored relation
2. B.Selects specific columns from a relation✓ Correct
3. C.Joins two relations on common attributes
4. D.Selects specific rows from a given relation

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Q3. The union of two relations R and S contains:

1. A.Only tuples that are common to both R and S
2. B.All tuples from both R and S without duplicates✓ Correct
3. C.The Cartesian product of relations R and S
4. D.Tuples in R but not present in relation S

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Q4. Which relational algebra operation renames a relation or its attributes?

1. A.Rename (ρ)✓ Correct
2. B.Projection (π)
3. C.Division (÷)
4. D.Selection (σ)

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Q5. The Cartesian product of relations R and S is denoted as:

1. A.R ∪ S
2. B.R × S✓ Correct
3. C.R ∩ S
4. D.R − S

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Q6. Set difference (R − S) returns:

1. A.Common tuples found in R and S
2. B.Tuples in S that are not in R
3. C.Tuples in R that are not in S✓ Correct
4. D.All tuples from both R and S

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Q7. For union compatibility, two relations must have:

1. A.The same number of attributes with compatible domains✓ Correct
2. B.The same name for both relations being combined
3. C.The same number of tuples stored in both relations
4. D.Identical primary keys defined on both data relations

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Q8. The intersection of R and S (R ∩ S) returns:

1. A.Tuples that are only in relation R
2. B.Tuples that are only in relation S
3. C.All tuples from relations R and S
4. D.Tuples that are in both R and S✓ Correct

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Q9. Which operation is fundamental in relational algebra (cannot be derived from others)?

1. A.Intersection
2. B.Division
3. C.Selection✓ Correct
4. D.Natural join

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Q10. The natural join operation:

1. A.Renames attributes within a relation for query convenience
2. B.Returns all tuples from both relations regardless of matching
3. C.Combines tuples from two relations based on common attributes✓ Correct
4. D.Removes duplicates from a single relation without conditions

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Q11. The theta join of relations R and S is:

1. A.A rename operation applied to change the relation name
2. B.A Cartesian product followed by selection with a condition✓ Correct
3. C.A set union combining all tuples from two given relations
4. D.A simple projection on selected attributes from the relation

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Q12. An equi-join is a special case of theta join where:

1. A.No condition is applied to the join result
2. B.The result of the join is always an empty set
3. C.The condition uses only inequality comparisons
4. D.The condition uses only equality comparisons✓ Correct

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Q13. The division operation R ÷ S returns:

1. A.The Cartesian product of both relations R and S fully
2. B.Tuples in R that are associated with every tuple in S✓ Correct
3. C.All tuples from relation S regardless of the condition
4. D.All tuples from relation R regardless of the condition

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Q14. Left outer join includes:

1. A.All tuples from the right relation and matching from the left side
2. B.Only tuples that have matching values in both of the joined tables
3. C.No tuples at all if there is no matching condition between tables
4. D.All tuples from the left relation and matching tuples from the right✓ Correct

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Q15. In relational algebra, which operation can be derived from the fundamental operations?

1. A.Projection
2. B.Intersection✓ Correct
3. C.Division
4. D.Selection

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Q16. The semi-join of R and S returns:

1. A.All tuples from both relations R and S combined
2. B.The complete Cartesian product of R and S result
3. C.Only the tuples from relation S not in relation R
4. D.Tuples from R that have matching tuples in S✓ Correct

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Q17. Anti-join of R and S returns:

1. A.All tuples from R regardless of matching in S
2. B.The complete Cartesian product of R and S both
3. C.Tuples from R that have no matching tuples in S✓ Correct
4. D.All tuples that match between relations R and S

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Q18. Relational calculus is:

1. A.A procedural query language that specifies how to retrieve data
2. B.A data definition language for creating tables and constraints
3. C.A physical storage language for defining data file structures
4. D.A non-procedural query language that describes what to retrieve✓ Correct

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Q19. Tuple relational calculus uses:

1. A.Tuple variables that range over relations✓ Correct
2. B.Domain variables that range over values
3. C.Only table names without any variables
4. D.No variables of any kind are required

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Q20. Domain relational calculus uses:

1. A.SQL queries written in standard syntax format
2. B.No variables of any kind within the expression
3. C.Domain variables that range over attribute domains✓ Correct
4. D.Tuple variables that range over entire relations

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Q21. A query language is relationally complete if it can express:

1. A.All queries expressible in relational calculus✓ Correct
2. B.Only join operations between related tables
3. C.Only aggregate functions on grouped data
4. D.Only selection and projection operations used

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Q22. The aggregate operation in extended relational algebra:

1. A.Performs Cartesian products between two unrelated relations
2. B.Renames relations and their associated attributes in queries
3. C.Selects individual tuples based on a simple filter condition
4. D.Computes functions like SUM, AVG, COUNT on groups of tuples✓ Correct

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Q23. Which of the following cannot be expressed in basic relational algebra?

1. A.Projection of attributes from relations
2. B.Selection with various filter conditions
3. C.Recursive queries like transitive closure✓ Correct
4. D.Natural join of two compatible relations

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Q24. The concept of safe expressions in relational calculus ensures:

1. A.Queries always run faster than other approaches
2. B.No NULL values appear in the query results
3. C.All tuples in the relation are always selected
4. D.The result of a query is a finite set of tuples✓ Correct

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Q25. In tuple relational calculus, the expression {t | P(t)} means:

1. A.Update tuples in the relation where P is a false value
2. B.Delete all tuples from the relation where P is true value
3. C.The set of all tuples t such that predicate P(t) is true✓ Correct
4. D.Insert tuples into the relation that satisfy predicate P

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Q26. The outer union operation:

1. A.Only works with relations that have identical schemas and matching attributes
2. B.Is the same as regular union and produces exactly identical results every time
3. C.Takes the union of relations that are not union-compatible by padding with NULLs✓ Correct
4. D.Removes all NULL values from the result set after combining both relations

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Q27. Full outer join preserves:

1. A.Only tuples from the left relation with NULL for non-matching rows
2. B.Only tuples from the right relation with NULL for non-matching rows
3. C.All tuples from both relations, padding with NULLs where necessary✓ Correct
4. D.Only tuples that have matching values in both of the joined tables

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Q28. The multiset (bag) version of relational algebra differs from set-based algebra in that:

1. A.It removes all duplicates
2. B.It allows duplicate tuples✓ Correct
3. C.It does not support joins
4. D.It only supports selection

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Q29. Which algebraic equivalence rule is used for query optimization?

1. A.Removing all joins from the query plan
2. B.Pushing selections down the query tree✓ Correct
3. C.Eliminating projections from the query
4. D.Reversing the order of query operations

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Q30. The assignment operation in relational algebra is used to:

1. A.Delete relations permanently from the database schema and storage system
2. B.Assign the result of a relational algebra expression to a temporary variable✓ Correct
3. C.Modify existing tuples by updating their attribute values in the table
4. D.Create new databases and define their schema structure from scratch

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