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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
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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.

edited
+1
Yes. In (b) a is not repeating and so, FD trivially holds. In all other options, FD condition is easily violated.

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

Ans: B YZ → X and Y → Z