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Third Normal Form
Decomposition into 3NF
B is in
- Assume is not a superkey
- must contain some attribute not in
- Since B is in F+ it must be derivable from Fc, by using attribute closure on
- Attribute closure cannot have used
- if it had been used, must be contained in the attribute closure of , which is not possible, since we assumed is not a superkey
- Now, using (- {B}) and B, we can derive B (since , and since B is non-trivial)
- Then, B is extraneous in the right-hand side of ; which is not possible since is in Fc
- Thus, if B is in then must be a superkey
Notes: