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Consider the following relation schema R(A, B, C, D, E, F) with the following functional dependencies: AC-gt;F, B -gt;D, AB-gt;CEF, ACE-gt;B, and...

Consider the following relation schema R(A, B, C, D, E, F) with the following functional dependencies: AC->F, B ->D, AB->CEF, ACE->B, and AEF->BC. Please complete the following: 

  1. Give all the candidate keys for relation schema R(A, B, C, D, E, F) under the set of FDs. Please describe, illustrate, and explain your solution in detail. 
  2. Is Relation R in the 3rd Normal Form? If yes, why and explain in detail. If no, show which FD violates the 3NF condition and explain why in detail. 
  3. Is Relation R in BCNF? If yes, why and explain in detail. If no, show which FD violates the BCNF condition and explain why in detail. 
  4. Try to decompose relation schema into several relational schemas in BCNF. Please describe, illustrate, and explain why each decomposition step is desirable in detail.
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