Is F included in F+? The definition in my book says:


  The set of all functional dependencies logically implied by F is the closure of F.


My question is, do we include FDs in F in F closure as well ? 

If I have:


F = {A→B, B→C}
a) F+ = {A→C, A→BC, A→B, B→C}
b) F+ = {A→C, A→BC}


Which one would be correct a) or b) ?
Since each dependency implies itself (given the fact that in logic trivially every assertion implies itself), F is included in F+. But note that in your example F+ contains quite a large number of dependencies, in addition to the dependencies that you have listed, like for instance A→A, AB→C, B→B, AC→A, etc.