Relational database theory — evaluate the claim about keys: “A candidate key is a determinant that determines all the other columns in a relation.” Decide whether this statement is correct or incorrect, keeping in mind the formal definition of candidate key (minimal superkey) and functional determination of all attributes.
-
ACorrect — this statement is valid for candidate keys
-
BIncorrect — it confuses candidate key with foreign key
-
COnly sometimes correct — applies only when the key has a single attribute
-
DNot enough information — depends on normal form of the relation
-
EIrrelevant — candidate keys do not involve functional dependencies
Answer
Correct Answer: Correct — this statement is valid for candidate keys
Explanation
Introduction / Context: In the relational model, keys and functional dependencies describe how attributes (columns) relate. A candidate key is central to design because it uniquely identifies tuples (rows). This question asks whether a candidate key can be described as a determinant for all other columns in the relation.
Given Data / Assumptions:
- We are working with one relation (table) R.
- “Determines” refers to functional determination: X → Y means attributes X functionally determine attributes Y.
- “Candidate key” means a minimal superkey: it functionally determines every attribute in R and has no proper subset with that property.
Concept / Approach: A candidate key K is defined by two properties: uniqueness (K identifies each tuple) and minimality (no subset of K has the uniqueness property). Uniqueness in terms of dependencies means K → all attributes of R. Because K is minimal, removing any attribute from K breaks that determination. Therefore, calling a candidate key a “determinant of all other columns” is consistent with the formal definition.
Step-by-Step Solution:
Let K be a candidate key of relation R.By definition, K is a superkey ⇒ K → R (every attribute in R).By minimality, for any proper subset K', K' ↛ R.Hence K is indeed a determinant for all other attributes.Verification / Alternative check: Consider a Student(roll_no, name, program) relation where roll_no uniquely identifies each student. Then roll_no → name, program, and roll_no is minimal. This matches the claim precisely.
Why Other Options Are Wrong:
- “Incorrect — confuses with foreign key”: foreign keys reference keys in another relation and do not determine all columns here.
- “Only sometimes correct”: the property holds regardless of whether the key is single-attribute or composite.
- “Not enough information” and “Irrelevant” ignore the standard definition of a candidate key.
Common Pitfalls: Mixing up primary, candidate, and superkeys; forgetting the minimality part of the candidate key definition; assuming determination depends on normal form (it does not).
Final Answer: Correct — this statement is valid for candidate keys