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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
onsider the relation
$Student(stuid,dept,clsroll)$
The following functional dependencies are given:
$FD1: stuid \to dept$
$FD2: dept \to stuid$
$FD3: stuid \to clsroll$
$FD4: clsroll \to stuid$
$FD5: dept \to clsroll$
Which functional dependencies should be removed to obtain the canonical cover of the set?
A. FD2 and FD3
B. FD1 and FD5
C. FD5
D. FD1
Choose the correct answer from the options given below:
Solution
Given FDs:
$FD1: stuid \to dept$
$FD2: dept \to stuid$
$FD3: stuid \to clsroll$
$FD4: clsroll \to stuid$
$FD5: dept \to clsroll$
Check redundancy:
$FD5: dept \to clsroll$ can be derived as:
$dept \to stuid$ using $FD2$
$stuid \to clsroll$ using $FD3$
So,
$dept \to clsroll$
Therefore, $FD5$ is redundant.
Also, $FD2$ and $FD3$ can be removed together because:
$dept \to clsroll$ using $FD5$
$clsroll \to stuid$ using $FD4$
So,
$dept \to stuid$
Also,
$stuid \to dept$ using $FD1$
$dept \to clsroll$ using $FD5$
So,
$stuid \to clsroll$
Therefore, $FD2$ and $FD3$ are also removable together.
Hence, correct statements are A and C only.
So, correct option is:
$\boxed{(b)\ \text{A, C only}}$
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