Note: Each "Test Your Foundation Knowledge" post presents one or more misconceptions about data fundamentals. To test your knowledge, first try to detect them, then proceed to read our debunking, reflecting the current understanding of the RDM, distinct from whatever has passed for it in the industry to date. If there isn't a match, you can review references -- reflecting the current understanding of the RDM, distinct from whatever has passed for it in the industry to date -- which explain and correct the misconceptions. You can acquire further knowledge by checking out our POSTS, BOOKS, PAPERS, LINKS (or, better, organize one of our on-site SEMINARS, which can be customized to specific needs).

“...a Data Domain refers to all the valid values which a data element (column) may contain. The rule for determining the domain boundary may be as simple as a data type with a list of possible values. For example, a database table that has information about people, with one record per person, might have an "age" column. This gender column might be declared as a SMALLINT data type, and allowed to have a value between 0 and 120. The data domain for the age column is hence 0 - 120. In a normalized data model, the reference domain is typically specified in a reference table. Following the previous example, the age reference table could have exactly 120 records, one per allowed value. Reference tables are formally related to other tables in a database by the use of foreign keys. A better way would be to enforce the data domain through a check constraint. For example, the age column would require positive numeric values between 0 and 120. I have found that the best way to figure out all of your data domains and constraints is to spend some time designing and normalizing all of your tables.”
--Quora.com

Misconceptions

• There are no tables and, thus, no columns in relational databases;
• Domains are not (programming) data types;
• It is not the data model that is normalized;
• A referenced relation does not reference domains;
• A SQL CHECK constraint is not "better enforcement" of a referential constraint;
• Constraints are not determined BY logical design;
• Logical database design does not involve explicit normalization (to 1NF) or further normalization to 5NF.

Fundamentals

• Relational databases consist of relations with attributes defined on domains; tables with columns visualize relations with attributes, but play no part in the RDM.
• A relational domain represents a real world property and is a database object under DBMS control and, thus, is distinct from a programming data type which is an application object under programmer control that may not represent anything in the real world.
• 1NF (normalization) and 5NF (full normalization) are properties of relations (which comprise logical models), not of the data model (i.e., the RDM).
• An attribute which is a foreign key in a referencing relation references a primary key which is an attribute  in a referenced relation.
• A constraint can be expressed in syntactically different ways by a data sublanguage. The CHECK constraint is a syntactic alternative in SQL to declare referential constraints.
• Database relations are semantically constrained to be consistent with (i.e., represent faithfully) the corresponding conceptual model. Properties and properties in context (i.e., of specific entity types) are identified during conceptual modeling. Domain and attribute constraints respectively are specified during logical design to ensure consistency with the properties and properties in context they represent in the database.
• Database design that adheres the three principles mandated by the RDM produces 1NF and 5NF databases that do not require explicit normalization and further normalization.

Note: The difference between relational domains and programming data types are specified in Codd's RM/V2 book. SQL tables are not relations and SQL data types are not relational domains.


Recommended reading

Domains: The Database Glue

Understanding Domains and Attributes

The Interpretation and Representation of Database Relations