1. manufacturer,serialnum → model,batch,capacity,retailer
    2. model → manufacturer
    3. batch,manufacturer → model
    4. model → capacity
  1. 2NF. None of the left sides are proper subsets of a key (2NF is satisfied), but the last two FDs violate 3NF - batch,manufacturer and model are superkeys and model and capacity are not part of a key.

  2. Decompose to fix the 3NF problem:


    This is not BCNF because model is not a superkey in the relation that covers the FD model → manufacturer. Decomposing MODEL further, however, would mean that the FD batch,manufacturer → model is no longer covered by a relation. This is undesirable because it makes it more expensive to determine if database updates violate a dependency.