Normalization quiz, Normal form quiz in DBMS
1. We would say that {A1,
A2, …, An}+ is the set of all attributes of R
if and only if (A1, A2, …, An) is a
____________ for R.
[a] Primary key [b] Candidate key
[c] Super key [d] All of the above
Answer: [d] All of the
above
If the closure of set of attributes
includes all attributes then we would say that the set of attributes in
question forms the key.
2. Consider a relation R(A, B, C, D,
E) with FDs {A → BC, CD → E, B → D, E → A}. Are the relations R1(A,
B, C) and R2(A, D, E) resulted in a lossless join decomposition of
R?
Answer: YES
A decomposition of R into R1
and R2 is said to be lossless join decomposition if either of the
following two conditions hold;
R1 ⋂ R2 → R1
R1 ⋂ R2 → R2
As per the given question, (ABC) ⋂ (ADE) = A. A is
the candidate key for R1 from the FD A → BC, hence the first condition holds. So,
the decomposition is lossless join decomposition.
3. Consider a relation R(A, B, C, D,
E) with FDs {A → BC, CD → E, B → D, E → A}. Are the relations R1(A,
B, C) and R2(C, D, E) resulted in a lossless join decomposition of
R?
Answer: NO
Refer answer 2 above for rules
As per the given question, (ABC) ⋂ (CDE) = C. From
the given FDs it is clear that C alone does not uniquely identify any
attributes of R. C is not a candidate key for either of the relations. So, the
decomposition is not lossless join decomposition.
4. Let us suppose that relations R
and S have r and s number of tuples (records) respectively. What are the
minimum and maximum numbers of tuples that R ⋈ S have?
[a] 0, rs [b] 1, rs
[c] r-s, rs [d] r-s, r+s
Answer: [a] 0, rs
The operation R Natural Join S
results in any tuple if at least one record of R and one record of S satisfy
the join condition.
Minimum – If no records satisfy the join
condition, the result will be 0 (Zero).
Maximum – If all the records of R
can be joined with all the records of S, then the result will be r*s.
5. Assume a relation R(A, B, C) with
the records (1, 2, 3), (4, 2, 3), (5, 3, 3), (5, 3, 4). Which of the following FDs
is/are true?
[a] A → B [b] BC → A
[c] B → C [d] None of the above.
Answer: [a] A
→ B