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The best normal form of relation scheme $R(A, B, C, D)$ along with the set of functional dependencies $F = \left\{AB \rightarrow C, AB \rightarrow D, C \rightarrow A, D \rightarrow B\right\}$ is

  1. Boyce-Codd Normal form
  2. Third Normal form
  3. Second Normal form
  4. First Normal form 
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keys are AB,CD,BC,AD

Here A,B,C,D all are prime attributes

So, no partial or transitive dependency are there

Therefore it is in 3NF

but as C and D are not keys for the relation A,B,C,D , therefore it is not in BCNF
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