Q8.Marks: +2.0UGC NET Paper 2: Computer Science 11 March 2023
Which of the following statement is correct, according to the following instance of the relational schema R(X, Y, Z)?
X
Y
Z
1
1
a
1
1
a
2
1
b
3
2
b
1.X →Y, Z → X
2.Y → Z, Z → X
3.X → Y, X → Z ✓ Correct
4.Y → X, X → Z
Solution
The correct answer is X → Y, X → Z
Key PointsA functional dependency, denoted X → Y, refers to a relationship between two sets of attributes. If X → Y, this means that for all tuples in a relation, if two tuples have the same value for the set of attributes X, they must also have the same value for the set of attributes Y. Similarly, for Y → X, if two tuples have the same Y value, they must have the same X value.
X
Y
Z
1
1
a
1
1
a
2
1
b
3
2
b
Let's analyze the four options:
X → Y, Z → X: X is functionally dependent on Y because it is uniquely identify Y value but Z does not hold true because Z is not functionally dependent on X. so it is incorrect .
Y → Z, Z → X: Y does not determine Z uniquely so it is also incorrect.
X → Y, X → Z: X is functionally dependent on Y because it is uniquely identify Y value and X is functionally dependent on Z because it is uniquely identify Z value. So, both functional dependency are correct.
Y → X, X → Z: Y does not determine X uniquely so it is also incorrect.
