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## NPTEL Introduction to Database Systems Assignment 3 Answers 2023:

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#### Q.1. Which of the following statements about the relational model is/are incorrect ?

- A key can not be determined from any particular instance data.
- Some relations may not have a foreign key.
**Some relations may not have a key.**- A key of a relation may have more than one attribute.

#### Q.2. Consider the following statements about relational model and find TRUE ones:

- The join relational algebra operator can NOT be expressed using other operators.
**The cross product relational algebra operator requires its operands to be union-compatible.**- The difference relational algebra operator requires its operands to be union-compatible.
- When project is applied on an instance r, the size of the result will always be the same as that of r.

#### Q.3. Suppose A is a foreign key in a relation R that refers to tuples of relation S using values of the key attribute B of S. Let X be the set of all non-null values of column A and let Y be the set of all values of column B. Identify the correct relationship between X and Y that holds on all instances of R and S:

**X is a subset of Y**- X is a proper subset of Y
- Y is a subset of X
- X need not be a subset of Y and Y need not be a subset of X

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#### Q.4. The join operation on two relations can be equivalently realised by doing

**A cartesian product of the two relations followed by a selection**- A cartesian product of the two relations
- A union of the two relations followed by a selection
- A union of two relations

#### Q.5. Consider the following relations S1( A, B, C, D ) and S2( E, F, G, H ) and the given instances. What is the result of the relational algebra expression:

**Π _{A,B} ( σ_{(C = 3)⋁(D = 1)} (S1) ) − Π_{E,F} ( σ_{(G ≠ 2)⋁( H ≠ 3)} (S2) )**

- Empty relation
- { (1,2), (3,6) }
- A relation with scheme (A,B) and tuples { (1,2) }
**A relation with scheme (A,B) and tuples { (1,2), (2,5), (3,6) }**

#### Q.6. Using the relations in Question 5. Find out how many tuples will be there in the result of the following relational algebra expression.

**S1⋈(S1.B>S2.H)S2�1⋈(�1.�>�2.�)�2**

- 2
**7**- 8
- 10

#### Q.7. Consider the following three relations in a relational database.

Employee(eId, Name), Brand(bId, bName), Own(eId, bId)

Which of the following relational algebra expressions return the set of eids of employees who own all the brands?

**Answer: A**

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#### Q.8. Given the relations

Employee( eid, name, salary, dept-no)

Department( dept-no, dept-name, address)

Which of the following queries **cannot** be expressed using the basic relational algebra operations ( σ, Π, ✕, ⋈, ⋃, ⋂, 一 ) ?

- Department address of every employee
- Employees whose name is the same as their department name.
**The sum of the salary values of all employees.**- All employees of a given department.

#### Q.9. The following relation records the age of 500 employees of a company

empAge(empNo, age)

Consider the following relational algebra expression:

Π_{empNo}( empAge ⋈_{(age > age1)}ρ_{empNo1,age1}(empAge))

What does the above expression generate?

- Employee numbers of only those employees whose age is the maximum.
**Employee numbers of only those employees whose age is more than the age of exactly one other employee.**- Employee numbers of all employees whose age is not the minimum.
- Employee numbers of all employees whose age is the minimum

#### Q.10. Consider the join of a relation R with a relation S. If R has m tuples and S has n tuples then the maximum and minimum sizes of the result of a join, respectively, are:

S1: The key of an entity type always consists of more than one attribute.

S2: An entity type has exactly one key.

S3: An entity type may have more than one key.

Choose the correct option:

- m+n and 0
**mn and 0**- m+n and |m−n|
- mn and m+n

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#### About NPTEL Introduction to Database Systems Course:

Databases are the backbone of almost all the digital services and e-governance solutions. Modern businesses and financial systems heavily depend on databases systems and transaction processing for their successful operation. This course introduces the students to the various theoretical and practical principles involved in the design and use of databases systems with the help of database management systems (DBMS) and the SQL Standard

##### Course Outcome:

**Week 1**: Introduction and part of E/R Model Module**Week 2**: ER Model Module**Week 3**: Relational Model Module**Week 4**: Relational Model Module**Week 5**: TRC Module and part of SQL Module**Week 6**: SQL Module**Week 7**: Indexes Module**Week 8**: Indexes Module + Query Processing Module**Week 9**: Normal Forms Module**Week 10**: Normal Forms Module**Week 11**: Transaction Processing Module**Week 12**: Transaction Processing Module

**CRITERIA TO GET A CERTIFICATE**:

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.

Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

**YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.**

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