Consider a decomposition R 1 ,...,R n of R obtained via steps 1, 2, and 3 (but not step 4) of the 3NF synthesis algorithm. Suppose there is an attribute A in R that does not belong to any of the R , i =1,...,n. Prove that A must be part of every key of R. i

What will be an ideal response?

If A does not occur in any of the schemas constructed via the steps 1,2,3 of the 3NF synthesis algorithm, it means that A does not occur in any of the FDs in the minimal cover of the FDs of the schema. Therefore, there is no way by which A might be in the
attribute closure of an attribute set that does not contain A.