Let R (A1, A2, A3, A4) be a relation and F be a set of functional dependencies among attributes {A1, A2, A3, A4} such that: 

• {A1, A2, A3, A4}+ = {A1, A2, A3, A4} 

• no proper, nonempty subset of {A1, A2, A3, A4} is equal to its closure with respect to the set F of functional dependencies. 

What is the set F of functional dependencies in R (compatible with the two conditions above) ? Show the full details of your work.