Every relation that is in BCNF is necessarily also in third normal form.
Answer: A
Correct answer: True
The normal forms are nested: BCNF is strictly stronger than 3NF, so satisfying it implies satisfying 3NF. The converse does not hold, since a 3NF relation with overlapping candidate keys can still violate BCNF.
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Relations are categorized into normal forms according to the referential integrity constraints that they have.
Answer: B
Correct answer: False
Normal forms are defined by the functional and multivalued dependencies a relation permits, not by referential integrity constraints. Referential integrity is a constraint between relations, requiring foreign key values to exist in the referenced relation, and it is entirely independent of how far a relation has been normalised.
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Keys made up of two or more attributes are called composite keys.
Answer: A
Correct answer: True
A composite key is simply a key made up of more than one attribute, used where no single attribute is unique on its own - a line item identified by order number together with line number, for instance. It is still a key in every respect and must still be minimal, so that no constituent attribute could be removed.
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Which of the following is not a restriction for a table to be a relation?
Answer: C
Correct answer: The columns must be ordered.
Column order is precisely what a relation does not require: attributes are identified by name, so the columns may be written in any sequence without changing the relation. The other three are genuine requirements - single-valued cells, homogeneous columns, and no duplicate rows - and a table that breaks any of them is not a relation.
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In a relation, the rows are sometimes called "records."
Answer: A
Correct answer: True
The vocabularies correspond directly: relation, tuple and attribute in the formal relational terminology are table, record and field in the older file-processing one. The terms are used interchangeably in practice, and being fluent in both matters because textbooks and product documentation mix them freely.
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If attribute A determines both attributes B and C, then it is also true that:
Answer: A
Correct answer: A → B.
If A determines the pair (B, C), then it determines each of them separately: given a value of A, the value of B is fixed and so is the value of C. This is the decomposition rule of Armstrong’s axioms. The converse does not hold, so nothing follows in the reverse direction, and the other three options all reverse the arrow.
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A key is a group of one or more attributes that uniquely identifies a row.
Answer: A
Correct answer: True
This is the definition of a key. It may consist of a single attribute or of several, in which case it is a composite key, and it must be minimal, so that dropping any attribute from it would destroy uniqueness. A relation may have several such candidate keys, one of which is chosen as the primary key.
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The functional dependency R → S means that the value of S can be determined when we are given a value of R.
Answer: A
Correct answer: True
This is the definition. R → S asserts that each value of R is associated with exactly one value of S, so knowing R is enough to determine S. R is the determinant, S the dependent attribute. It is a statement about the meaning of the data, so no set of sample rows can prove it - a single counterexample refutes it.
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For some relations, changing the data can have undesirable consequences called:
Answer: B
Correct answer: modification anomalies.
A poorly structured relation makes some changes impossible to perform cleanly: an insertion anomaly prevents a fact being recorded until some unrelated fact is known, a deletion anomaly destroys information as a side effect, and an update anomaly requires the same value to be changed in many places. Normalisation exists to remove them.
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In a relation, the order of the columns does not matter.
Answer: A
Correct answer: True
Attributes are identified by name, so writing the columns in a different order produces the same relation. The same is true of rows, which form a set and so have no inherent order either. Both facts follow from the relation being defined by its content rather than by any arrangement of it.
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