Which one of the following statements regarding operations on relations in a database is FALSE?

a$.$ The difference operation is applied to two relations that do not necessarily have the same attributes.

b$.$ The difference between the join and union operations is that with the join operation the two relations are combined based on common attributes, while with the union operation, the two relations must have exactly the same attributes.

c$.$ The project operation creates another relation in which each tuple in the resulting relation has fewer attributes than the corresponding tuple in the original relation.

d$.$ The intersection operation creates a new relation from two relations with the same attributes, where the new relation contains tuples which are members of both original relations.