I am trying to understand what are the steps to check if a decomposition of table is in 3NF.

There is a specific exercise I'm trying to solve with no success.

  • Given that R={A1,A2,A3,A4}
  • and F={A1→A2A3A4,A2→A3,A3→A4,A4→A2}

The decomposition is:

  • R1={A1,A4}
  • R2={A4,A2}, A3={A2,A3}

(super keys are shown in bold)

According to the answers this decomposition is not in 3NF.

Unfortunately, I cant understand why. My main difficulty is the transitivity check, and a couple of questions have arisen:

  1. Should I check transitivity per table?

  2. While doing that should I ignore every dependency in ab in F if a or b does not exist in the table?

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