Should a database table that contains two columns that are foreign keys have a third column which is the primary key?

In theory, if the combination of the two foreign keys (FKs) is unique in the table, or if the combination of the two FKs plus some other column is unique, then the table has a compound primary key and there is no strict need to introduce another key as a surrogate primary key. However, it is not unusual to find that people do add an extra key. In part, it depends on what else the data in the table with the compound primary key will used for.

If it describes something that will itself have rows from other tables associated with it, then it may make sense to introduce a simple PK.

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