Applying the union rule to the given question, we get, A→BC is true. The other two options are specified in the question itself.

All functional dependencies are transitive. This is the transitivity rule of Armstrong’s axioms.

A Canonical cover Fc for F is a set of dependencies such that F logically implies all dependencies in Fc, and Fc logically implies all dependencies in F. In Fc, no functional dependency should contain an extraneous attribute and each left side of functional dependency should be unique.

Armstrong’s axioms allow us to generate all F+ for any given F and hence are called complete.

We say that a decomposition having the property F’+ = F+ is a dependency preserving decomposition.

Armstrong’s axioms are called as sound axioms because they do not generate incorrect functional dependencies.

Given a set F of functional dependencies on a schema, we can prove that certain other functional dependencies also hold on that schema. We say such FDs are logically implied by F. A functional dependency f on R is logically implied by a set of functional dependencies F on r if every instance of r(R) that satisfies F also satisfies f.

If a functional dependency is reflexive, B is a subset of A and A is the set of attributes, then A→B holds. This is called the reflexivity rule of Armstrong’s axioms.

If F is a set of functional dependencies, then the closure of F is denoted by F+. It is the set of all functional dependencies logically implied by F.

If B is an attribute and A→B, Then B is said to be functionally determined by a.