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+17 votes

Given the following relation instance.

                X      Y      Z 
                1      4      2 
                1      5      3 
                1      6      3 
                3      2      2

Which of the following functional dependencies are satisfied by the instance?

  1. XY → Z and Z → Y                                      
  2. YZ → X and Y → Z
  3. YZ → X and X → Z                                    
  4.  XZ → Y and Y → X
asked in Databases by Veteran (59.9k points)
edited by | 2.3k views

4 Answers

+28 votes
Best answer

(b) is answer.

If $a->b$ then for each same value of $a$, $b$ should be same,

We have to get the opposite of the defn i.e if no values of $a$ are same then $b$ need be same.

answered by Active (3.3k points)
edited by
Yes. In (b) a is not repeating and so, FD trivially holds. In all other options, FD condition is easily violated.
+14 votes

Option B is correct.

a functional dependency A \rightarrow B is said to hold if for two tuples t1 and t2 . If for t1[A] = t2[A] then t1[Y] = t2[Y].

Here we can manually check for each option with the given instance and option B satisfies

answered by Boss (11.6k points)
+5 votes

Answer should be (B). 

YZ->X and Y->Z. Here YZ uniquely determines X and Y uniquely determines Z. 


answered by Active (1.7k points)
edited by
–2 votes
Ans: B YZ → X and Y → Z
answered by Loyal (7.8k points)

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