In database management systems, what is a candidate key and how is it defined?

Introduction / Context:
Relational database design relies on different types of keys to enforce uniqueness and define relationships. Candidate keys play a central role in determining which fields can uniquely identify rows. This question checks whether you understand what a candidate key is and how it relates to primary keys.

Given Data / Assumptions:

• We are discussing a single relation or table in the relational model.
• Each row in the table must be uniquely identifiable.
• There may be more than one possible set of attributes that can uniquely identify rows.
• The options describe different possible interpretations of the term candidate key.

Concept / Approach:
A candidate key is a minimal set of attributes that uniquely identifies each tuple in a relation. Minimal means that if you remove any attribute from the set, it no longer uniquely identifies rows. A table can have multiple candidate keys. One of these is chosen as the primary key, and the others are often referred to as alternate keys. This definition distinguishes candidate keys from superkeys, which may contain extra attributes, and from non unique or purely indexing columns.

Step-by-Step Solution:
Step 1: Recall that a superkey is any set of attributes that uniquely identifies rows, possibly including unnecessary attributes. Step 2: Recognize that a candidate key is a superkey with the minimal number of attributes needed for uniqueness. Step 3: Understand that the primary key is selected from among the candidate keys for implementation convenience or design reasons. Step 4: Compare this definition with the options and observe that option a exactly states that a candidate key is a minimal set of attributes that uniquely identifies tuples and can be chosen as a primary key. Step 5: Confirm that options describing duplicate containing sets, sorting attributes, or backup copies do not match the formal definition.

Verification / Alternative check:
Consider a table students with attributes (student_id, email, phone_number, name). If both student_id and email are unique for each student, then {student_id} and {email} are candidate keys. They are minimal and uniquely identify each row. The designer may choose student_id as the primary key and treat email as an alternate key. This example illustrates the role of candidate keys in schema design.

Why Other Options Are Wrong:
Any combination of columns that may contain duplicate values and is used only for indexing describes performance related indexes, not candidate keys. Any attribute that appears in the WHERE clause of a query, regardless of uniqueness, is unrelated to the formal notion of keys. A column used only for sorting rows in the output without guaranteeing uniqueness may be included in ORDER BY but is not a key. A backup copy of the primary key stored in a different table refers to redundancy for recovery, not to the formal key concept.

Common Pitfalls:
Learners sometimes confuse candidate keys with primary keys and think there can be only one candidate key in a table. Another mistake is ignoring minimality, which can lead to describing large attribute sets as keys even when smaller subsets are sufficient. In design work, identifying all candidate keys helps you choose an appropriate primary key and understand potential unique constraints.

Final Answer:
A candidate key is a minimal set of attributes that can uniquely identify each tuple in a relation and from which a primary key can be chosen.