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# Multiple choice questions with answer on normalization process and join operations in database management systems for exams

## MCQ on DBMS - Normalization and Join operations

1. Consider Relation R(ABCD) and functional dependencies (FDs): BD → AC; AB → D; AC → B. Which of the following is a candidate key of R?
a) AB
b) BD
c) AC
d) All of the above

 Answer: (d) All of the above To check for a candidate key, let us find the closure of these attribute sets as follows; (AB)+ is the closure of (AB). This can be calculated using the given set of FDs.             AB+    = ABD from FD AB → D                         = ABDC from FD BD → AC                         = ABCD = R As the closure of AB includes all attributes from R, AB is a candidate key.             BD+    = ABCD through FD BD → AC             AC+    = ABCD through FDs AC → B and AB → D

2. Consider two relations R(a,b,c) and S(a,d,e). T(R)=200, T(S)=100. R.a is a foreign key referencing S.a and S.a is the primary key of S. What is the estimated size of R S?
a) 100
b) 150
c) 200
d) 300

 Answer: (c) 200 Given, S.a is the primary key and R refers it through R.a. Natural join works on equivalence of common attributes. Foreign key ensures values only from the primary key table, in our case it is S. Foreign key table has 200 records that are valid. Hence, the join will result in 200 records.

3. Consider relation R(A, B) and S(B, C), where T(R) = 200 and T(S) = 100, and B is a key for R. What is the estimate for T(R S)?
a) 100
b) 150
c) 200
d) 300

 Answer: (a) 100 Given, Attribute B is the primary key for R. In that case, S.B must be the foreign key that refers R.B. Maximum matching number of records are the records of foreign key table. Hence, only 100 records are possible as maximum as the result of R ⨝ S.

4. Consider a relational schema R(A, B, C). Let us suppose that we decompose R into R1(A, B), and R2(A, C). Is this decomposition always lossless?
a) Yes
b) No
c) Depends on FDs
d) Cannot determined

 Answer: (c) Depends on FDs We cannot determine whether the decomposition is lossless or not without set of functional dependencies hold one the given relation. Refer here for How to find whether the decomposition is lossless or not? http://www.exploredatabase.com/2016/04/define-lossless-join-decomposition-with-example.html http://www.exploredatabase.com/2016/11/is-given-decomposition-is-lossless-join-decomposition.html

5. Let R(A, B, C, D, E, F) be a database schema with set F of functional dependencies F = {AB → C, BC → AD, D → E, CF → B}. What is the closure of AB?
a) ABC
b) ABCD
c) ABCDE
d) ABCDEF

 Answer: (c) ABCDE To find the closure of the given set of attributes; (AB)+ is the closure of (AB). This can be calculated using the given set of FDs.             AB+    = ABC from FD AB → C                         = ABCD from FD BC → AD                         = ABCDE from FD D → E                         = ABCDE because no more FDs that have one of these attributes on the LHS. http://www.exploredatabase.com/2016/12/closure-in-database-home-page.html

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