Advanced Relational Algebra and Relational Calculus MCQs

Question 1

Which algebraic operation in relational algebra can be used to combine the results of

o A) UNION
o B) INTERSECT
o C) DIFFERENCE
o D) JOIN

Answer 1

UNION

Question 2

What is the result of the operation R ∪ R where R is a relation?

o A) R
o B) R with duplicates removed
o C) An empty relation
o D) A relation with double the tuples of R

Answer 2

R

Question 3

Which of the following statements is true regarding the Cartesian product?

o A) It combines two relations based on a common attribute.
o B) It returns all combinations of tuples from two relations.
o C) It removes duplicates from the resulting relation.
o D) It is equivalent to an INNER JOIN.

Answer 3

It returns all combinations of tuples from two relations.

Question 4

In tuple relational calculus, which of the following is a valid expression?

o A) {t | t ∈ Students AND t.GPA > 3.5}
o B) SELECT * FROM Students WHERE GPA > 3.5
o C) Students ∩ Graduates
o D) ALL OF THE ABOVE

Answer 4

{t | t ∈ Students AND t.GPA > 3.5}

Question 5

What is the main limitation of relational calculus compared to relational algebra?

o A) It cannot express complex queries.
o B) It is more procedural.
o C) It lacks the ability to perform aggregations.
o D) It is less intuitive.

Answer 5

It lacks the ability to perform aggregations.

Question 6

Which of the following operations can be expressed using relational algebra but not relational calculus?

o A) JOIN
o B) SELECT
o C) PROJECT
o D) All of the above

Answer 6

All of the above

Question 7

In relational algebra, what does the expression R - S represent?

o A) The intersection of R and S
o B) The union of R and S
o C) The tuples in R that are not in S
o D) The Cartesian product of R and S

Answer 7

The tuples in R that are not in S

Question 8

What is the significance of the term “closure” in the context of functional dependencies?

o A) It represents the set of all attributes that can be functionally determined.
o B) It indicates the completeness of a relation.
o C) It refers to the elimination of duplicates.
o D) It is a method for optimizing queries.

Answer 8

It represents the set of all attributes that can be functionally determined.

Question 9

Which type of join will produce the largest result set?

o A) INNER JOIN
o B) LEFT JOIN
o C) RIGHT JOIN
o D) CROSS JOIN

Answer 9

CROSS JOIN

Question 10

In relational algebra, what is the result of the expression R ⋈ S if R and S have no common attributes?

o A) A relation with attributes from both R and S
o B) An empty relation
o C) A relation with attributes from R only
o D) A relation with attributes from S only

Answer 10

A relation with attributes from both R and S

Question 11

Which of the following statements about relational calculus is true?

o A) It is procedural and requires an algorithm to execute.
o B) It is a declarative language that specifies what to retrieve rather than how to retrieve it.
o C) It cannot express queries involving aggregates.
o D) It is less powerful than relational algebra.

Answer 11

It is a declarative language that specifies what to retrieve rather than how to retrieve it.

Question 12

What does the term “domain restriction” refer to in relational calculus?

o A) The use of specific domains in attributes
o B) Limiting the result set to specific values for an attribute
o C) Restricting the types of operations that can be performed
o D) Defining the schema of a relation

Answer 12

Limiting the result set to specific values for an attribute

Question 13

Which operation can be used to find common tuples in two relations?

o A) UNION
o B) INTERSECT
o C) DIFFERENCE
o D) JOIN

Answer 13

INTERSECT

Question 14

What does the expression σ_A=10(R) return?

o A) All tuples in R
o B) Tuples from R where attribute A equals 10
o C) The distinct values of A in R
o D) A count of tuples in R with A = 10

Answer 14

Tuples from R where attribute A equals 10

Question 15

Which of the following is an advantage of using relational algebra over relational calculus?

o A) It is easier to understand.
o B) It can express a wider range of queries.
o C) It provides a procedural approach to query execution.
o D) It is better for academic purposes.

Answer 15

It provides a procedural approach to query execution.

Question 16

In tuple relational calculus, which symbol is used to denote the universal quantifier?

o A) ∃
o B) ∀
o C) ∈
o D) ⊆

Answer 16

∀

Question 17

What does the expression π_A(R) ∩ π_A(S) represent?

o A) The union of attributes A from R and S
o B) The intersection of attributes A from R and S
o C) The difference of attributes A from R and S
o D) The Cartesian product of attributes A from R and S

Answer 17

The intersection of attributes A from R and S

Question 18

Which of the following can be considered a valid relational calculus expression?

o A) {t | t ∈ Students AND t.Age > 20}
o B) Students WHERE Age > 20
o C) SELECT * FROM Students WHERE Age > 20
o D) ALL OF THE ABOVE

Answer 18

{t | t ∈ Students AND t.Age > 20}

Question 19

What is the result of the expression R ⋈ S if R has 10 tuples and S has 5 tuples, and they join on a common attribute with 3 matching values?

o A) 15 tuples
o B) 30 tuples
o C) 3 tuples
o D) 5 tuples

Answer 19

30 tuples

Question 20

Which operation in relational algebra is used to rename a relation or its attributes?

o A) SELECT
o B) PROJECT
o C) RENAME
o D) JOIN

Answer 20

RENAME

Question 21

What is the difference between INNER JOIN and OUTER JOIN?

o A) INNER JOIN returns all records; OUTER JOIN returns only matching records.
o B) INNER JOIN returns only matching records; OUTER JOIN returns all records.
o C) They are the same.
o D) INNER JOIN cannot be used with more than two tables.

Answer 21

INNER JOIN returns only matching records; OUTER JOIN returns all records.

Question 22

In relational calculus, which of the following is a valid way to express “find all students with a GPA above 3.0”?

o A) {s | s ∈ Students AND s.GPA > 3.0}
o B) SELECT * FROM Students WHERE GPA > 3.0
o C) Students WHERE GPA > 3.0
o D) ALL OF THE ABOVE

Answer 22

{s | s ∈ Students AND s.GPA > 3.0}

Question 23

Which operation is used to perform a relational division in relational algebra?

o A) INTERSECT
o B) DIFFERENCE
o C) JOIN
o D) Not directly available; it must be expressed using other operations.

Answer 23

Not directly available; it must be expressed using other operations.

Question 24

What is the significance of the HAVING clause in SQL?

o A) It filters records before aggregation.
o B) It filters records after aggregation.
o C) It sorts the results.
o D) It joins two relations.

Answer 24

It filters records after aggregation.

Question 25

Which of the following is NOT a characteristic of relational algebra? ## Footnote o A) It is procedural. o B) It is declarative. o C) It uses mathematical operations. o D) It focuses on sets of tuples.

Answer 25

It is declarative.

Question 26

In relational algebra, what does the RENAME operation allow you to do? ## Footnote o A) Change the values of tuples o B) Change the name of a relation or its attributes o C) Filter the result set o D) Perform a join operation

Answer 26

Change the name of a relation or its attributes

Question 27

In which scenario would you typically use a LEFT JOIN? ## Footnote o A) When you want only matching records from both tables. o B) When you want all records from the left table and matching records from the right. o C) When you want to combine data from two unrelated tables. o D) When you want to exclude all records from the left table.

Answer 27

When you want all records from the left table and matching records from the right.

Question 28

Which of the following is true about relational calculus? ## Footnote o A) It is less expressive than relational algebra. o B) It is only used for simple queries. o C) It can express all queries that relational algebra can express. o D) It requires procedural knowledge to use.

Answer 28

It can express all queries that relational algebra can express.

Question 29

What does the term "closure" refer to when discussing a set of functional dependencies? ## Footnote o A) The completion of a database o B) The set of all attributes that can be functionally derived from a given set o C) The removal of duplicate records o D) The final output of a query

Answer 29

The set of all attributes that can be functionally derived from a given set

Question 30

What does the expression R1 ⋈ R2 ON R1.A = R2.B indicate? ## Footnote o A) A cartesian product of R1 and R2 o B) An inner join between R1 and R2 based on the condition that R1.A equals R2.B o C) A union of R1 and R2 o D) A selection of R1 where R1.A equals R2.B

Answer 30

An inner join between R1 and R2 based on the condition that R1.A equals R2.B

Question 31

In relational calculus, what does the expression {t | t ∈ R AND P(t)} mean? ## Footnote o A) Select tuples from R that satisfy predicate P. o B) Select all tuples from R. o C) Select tuples from R that do not satisfy predicate P. o D) Select tuples based on an aggregate function.

Answer 31

Select tuples from R that satisfy predicate P.

Question 32

What is the result of a FULL OUTER JOIN between two relations? ## Footnote o A) Only the matching rows from both relations o B) All rows from both relations, with NULLs where there are no matches o C) A union of both relations o D) An intersection of both relations

Answer 32

All rows from both relations, with NULLs where there are no matches

Question 33

What does the expression π_A,B(R) perform? ## Footnote o A) Selects all attributes A and B from R o B) Projects only attributes A and B from relation R o C) Filters tuples based on attributes A and B o D) Joins relation R with itself

Answer 33

Projects only attributes A and B from relation R

Question 34

What would be the output of R ∩ S if R and S have no common tuples? ## Footnote o A) R o B) S o C) An empty relation o D) R ∪ S

Answer 34

An empty relation

Question 35

What is the purpose of using DISTINCT in a SQL query? ## Footnote o A) To sort the results o B) To remove duplicate rows from the result set o C) To limit the number of rows returned o D) To filter results based on conditions

Answer 35

To remove duplicate rows from the result set

Question 36

Which of the following relational algebra expressions would yield the same result? ## Footnote o A) π_Name(σ_Age>20(Students)) o B) σ_Age>20(π_Name(Students)) o C) Both A and B o D) None of the above

Answer 36

π_Name(σ_Age>20(Students))

Question 37

What is the main characteristic of the RENAME operation in relational algebra? ## Footnote o A) It does not change the number of rows. o B) It changes the values in tuples. o C) It allows for the creation of new relations. o D) It can only rename attributes, not relations.

Answer 37

It does not change the number of rows.

Question 38

In tuple relational calculus, what does the expression ∃x (P(x) ∧ Q(x)) mean? ## Footnote o A) For all x, P(x) and Q(x) are true. o B) There exists at least one x such that both P(x) and Q(x) are true. o C) Neither P(x) nor Q(x) is true for all x. o D) P(x) is true for all x.

Answer 38

There exists at least one x such that both P(x) and Q(x) are true.

Question 39

Which of the following is the primary advantage of relational calculus over relationalalgebra? ## Footnote o A) It is more procedural. o B) It is easier to optimize. o C) It allows for a clearer expression of queries without specifying how to execute them. o D) It can express all operations of relational algebra.

Answer 39

It allows for a clearer expression of queries without specifying how to execute them.

Question 40

What does the expression R - S represent in relational algebra? ## Footnote o A) The union of R and S o B) The intersection of R and S o C) The tuples in R that are not in S o D) The Cartesian product of R and S

Answer 40

The tuples in R that are not in S