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Consider a relation R=(M, N, O, P, Q) with the dependencies: {M,N ->O; O,P->Q ; P, Q-> N}. The key for relation R is :a.M, N, Ob.M, N, Pc.N, O, Pd.M, N

Question

Consider a relation R=(M, N, O, P, Q) with the dependencies: {M,N ->O; O,P->Q ; P, Q-> N}. The key for relation R is :a.M, N, Ob.M, N, Pc.N, O, Pd.M, N

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Solution

To find the key for the relation R, we need to find the minimal set of attributes that can determine all other attributes in the relation.

Step 1: Find the closure of each attribute set on the left side of the functional dependencies.

  • Closure of {M, N} is {M, N, O, Q} (using M,N ->O and O,P->Q)
  • Closure of {O, P} is {O, P, N, Q} (using O,P->Q and P, Q-> N)
  • Closure of {P, Q} is {P, Q, N} (using P, Q-> N)

Step 2: Check which closure set includes all attributes of the relation.

  • The closure of {M, N} does not include all attributes of the relation R. It is missing P.
  • The closure of {O, P} includes all attributes of the relation R.
  • The closure of {P, Q} does not include all attributes of the relation R. It is missing M and O.

So, the key for the relation R is {O, P}, which corresponds to option c. N, O, P.

This problem has been solved

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