Relational database theory: any table that meets the formal definition of a relation is, by definition, in First Normal Form (1NF). Is this statement accurate?

Introduction / Context:
First Normal Form (1NF) is the foundational requirement in relational database design. The statement claims that if a table meets the formal definition of a relation, then it is already in 1NF. Understanding what a “relation” means in the relational model clarifies why this is considered correct in most database textbooks and industry practice.

Given Data / Assumptions:

• A “relation” refers to the formal construct of the relational model, not just any arbitrary spreadsheet-like table.
• Attributes (columns) are defined over domains of atomic (indivisible) values.
• There is no inherent ordering of rows (tuples) or columns (attributes), and there are no duplicate rows in a relation.

Concept / Approach:
1NF requires that every attribute value is atomic (no repeating groups, no arrays in a single cell), and that the table behaves as a mathematical relation: unordered tuples, unordered attributes, and no duplicate tuples. The classical definition of a relation already encompasses atomic domains and these properties, so a structure that truly satisfies the definition of a relation is, by construction, in 1NF.

Step-by-Step Solution:

Verification / Alternative check:
Check any table: if a cell stores multiple values (e.g., comma-separated lists), it violates atomicity and thus fails to be a relation; therefore it also fails 1NF. Conversely, when all cells are single, indivisible values and other relation properties hold, it is considered 1NF.

Why Other Options Are Wrong:

• “Incorrect” contradicts standard theory equating relations with 1NF tables.
• “Applies only to primary keys” misunderstands that 1NF applies to all attributes, not only keys.
• “Depends on referential integrity only” confuses normalization with relationship constraints between tables.

Common Pitfalls:
Confusing a spreadsheet or denormalized table (with lists in cells) for a relation. Also, thinking that 1NF concerns foreign keys; it does not—those are separate design concerns.

Final Answer:
Correct