Let a prime attribute be one that appears in at least one candidate key. Let and

Let a prime attribute be one that appears in at least one candidate key. Let α and β be sets of attributes such that α → β holds but β → α do not hold. Let A be an attribute that is not in α, is not in β, and for which β → A holds. We say that A is transitively dependent on α. We can restate our definition of 3NF as follows: A relation schema R is in 3NF with respect to a set F of functional dependencies if there are no non prime attributes A in R for which A is transitively dependent on a key for R. Show that this new definition is equivalent to the original one.