The number of leaf nodes in a rooted tree of n nodes, with each node having 0 or 3 children is:

Relation $$R$$ with an associated set of functional dependencies, $$F,$$ is decomposed into $$BCNF.$$ The redundancy (arising out of functional dependencies) in the resulting set of relations is

From the following instance of a relation schema $$R(A, B, C),$$ we can conclude that:

Relation $$R$$ is decomposed using a set of functional dependencies, $$F,$$ and relation $$S$$ is decomposed using another set of functional dependencies, $$G.$$ One decomposition is definitely $$BCNF,$$ the other is definitely. $$3NF,$$ but it is not known which is which. To make a guaranteed identification, which one of the following tests should be used on the decompositions? (Assume that the closures of $$F$$ and $$G$$ are available).