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Consider the following constraints on a relation schema:

  • A student can register for at most $t$ courses and each course can have at most $p$ students.
  • Each student is enrolled to at least one course and each course has at least one student.

The schema is normalized into three tables:

  • Student,
  • Registers,
  • Courses

The number of tuples in student and course tables are $L$ and $Z$ respectively.

Which of the following is NOT possible?

  1. $Z = 1$
  2. $Z \leqslant t \times L$
  3. $L > p \times Z$
  4. $L \leqslant 10$
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Question says maximum t courses a student can register, Let us assume that there are 5 courses at max. so take t=5 ,

maximum p students can take  each course , so let p  = 2

for student table L is number of tuple so L = 5 ( as it is said at least one student per course ) and for courses table Z is number of tuples , so Z = 5 ( calculated from this line - Each student is enrolled to at least one course and each course has at least one student. )

now option A and D are true.

option A  must be TRUE if we assume there is at least one student .

option D  says L <=  10 so take L=5 which is < 10 so condition is True.


For option B ,

 Z <= t * L  put t =5 and Z = 5 and L = 5 it becomes 5<= 25 that is TRUE.

For option C ,

L >= p × Z   put L,p,Z value it becomes 5 >= 2 * 5   means 5 >= 10  that is False . 

Hence option C need not be correct.

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 take a random example. Here i have considered p=2 and t=2.

From table we can see L=3 Z=3

Z*p=6 which is greater than L.Hence C.

Answer:

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