Final answer:
A relation in 1st normal form automatically satisfies 2nd normal form if it has only one attribute as the primary key, as this eliminates the possibility of partial dependencies.
Step-by-step explanation:
The condition under which the 2nd normal form (2NF) is automatically satisfied when a relation is in the 1st normal form (1NF) concerns the existence of composite primary keys. In detail, a relation that is in 1NF will also be in 2NF if it does not have any composite primary keys, meaning the primary key consists of only one attribute. To reach 2NF, a relation must eliminate partial dependencies, which are dependencies where a non-key attribute is functionally dependent on part of a composite key. In cases where there is only a single-attribute primary key, partial dependencies are not possible, and thus, the requirement for 2NF is inherently met.
It is important to understand that for relations with a composite primary key, they must explicitly remove any partial dependencies to ensure they are in 2NF, which involves checking whether each non-key attribute is fully functionally dependent on the entire primary key.