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      Question

      Which functional dependency holds in given relation R

      (A, B, C) and why? Read the below passage and answer the questions Functional dependency A B means that B is dependent on A i.e. from the value of A we can find the value of B from the relation. Therefore, to prove A B holds in a relation, one of the following conditions must be true: Condition1: either all the value of A must be unique Or Condition2: all the value of B must be same Or Condition3: If two or more tuples/rows of the relation have same value for attribute A then there must be also same value for attribute B i.e. if t1[A] = t2[A] then there must be t1[B] = t2[B].
      A 1 Correct Answer Incorrect Answer
      B 2 Correct Answer Incorrect Answer
      C 3 Correct Answer Incorrect Answer
      D 4 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      AB ->C satisfies condition1 (all the values of AB are unique), but C->B does not satisfy any of the three conditions (C has not unique values, B has not all same values and the value of C is repeated two times (8, 5) then the value of B is not repeated), so option 1 is incorrect. B->C A satisfies condition1, and B-> C also satisfies condition1, so option 2 is correct. B->C A satisfies condition1, but A->C does not satisfy any of the three conditions, so option 3 is incorrect. A->C B does not satisfy any of the three conditions, and B-> C satisfies condition1, so option 4 is incorrect. Since BC ->A && B ->C holds in above relation, option 2 will be the answer.

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