HCU PHD CS 2018 June
October 31, 2024TIFR PHD CS & SS 2019
November 1, 2024Functional-Dependency
| Question 6 |
| (X,Y)→ (Z,W) implies X→ (Z,W) | |
| (X,Y)→ (Z,W) implies (X,Y)→ Z | |
| ((X,Y)→ Z and W→ Y) implies (X,W)→ Z
| |
| (X→Yand Y→ Z) implies X→ Z |
This statement is not necessarily true. The functional dependency (X,Y) → (Z,W) means that for any given value of X and Y, there is a unique value of Z and W. However, this does not imply that for any given value of X, there is a unique value of Z and W. So, option (A) is FALSE.
(B) (X,Y) → (Z,W) implies (X,Y) → Z
This statement is TRUE. If (X,Y) functionally determines (Z,W), then it also functionally determines Z. This is because for any given combination of X and Y, there is a unique value of Z according to the functional dependency. So, option (B) is TRUE.
(C) ((X,Y) → Z and W → Y) implies (X,W) → Z
This statement is TRUE. If X and Y together determine Z and W determines Y, then X and W together determine Z. This is because for any given combination of X and W, we can find the corresponding values of Y and then use (X,Y) → Z to determine the value of Z. So, option (C) is TRUE.
(D) (X → Y and Y → Z) implies X → Z
This statement is TRUE. If X determines Y and Y determines Z, then X determines Z. This is because the transitive property of functional dependency applies here. So, option (D) is TRUE
This statement is not necessarily true. The functional dependency (X,Y) → (Z,W) means that for any given value of X and Y, there is a unique value of Z and W. However, this does not imply that for any given value of X, there is a unique value of Z and W. So, option (A) is FALSE.
(B) (X,Y) → (Z,W) implies (X,Y) → Z
This statement is TRUE. If (X,Y) functionally determines (Z,W), then it also functionally determines Z. This is because for any given combination of X and Y, there is a unique value of Z according to the functional dependency. So, option (B) is TRUE.
(C) ((X,Y) → Z and W → Y) implies (X,W) → Z
This statement is TRUE. If X and Y together determine Z and W determines Y, then X and W together determine Z. This is because for any given combination of X and W, we can find the corresponding values of Y and then use (X,Y) → Z to determine the value of Z. So, option (C) is TRUE.
(D) (X → Y and Y → Z) implies X → Z
This statement is TRUE. If X determines Y and Y determines Z, then X determines Z. This is because the transitive property of functional dependency applies here. So, option (D) is TRUE