Can you determine a functional dependency on a single attribute table?

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Question :

If an attribute is independent is it possible for it to still have a functional dependency?

For example, given these were two tables with a many to many relation: Fruit(FruitType), Blender(BlenderNum,B,C,D,etc…), where Fruit has no other connecting relationship. I can make table Blends(FruitType, BlenderNum), both as primary key and drop the standalone Fruit table. Is there any functional dependency for the independent attribute Fruit now? It is not mentioned anywhere else in the database.

Blends(FruitType, BlenderNum*) – Blender(BlenderNum,B,C,D,etc…)

Answer :

In a relational model every relation describes one ‘thing’ – the ‘Fruits’ table models fruits, fruits are not blends. Your Fruits table with a single column, is all key – 5NF.
If you don’t have a Fruits table, how will you insert a new fruit which has no blend yet? What happens to a fruit you have in stock, but its blend is removed?

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