Test by Bikram | Databases | Test 1 | Question: 13

Question

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

This schema is normalized into three tables:
$\textbf{Student, Registers, Courses}$

The number of tuples in student and course tables are $X$ and $Y$ respectively. Which of the following need not be correct?

• A. $Y \geq 1$
• B. $Y \leq p ^* X$
• C. $X \geq v ^*  Y$
• D. $X > 0$

Comments

@Neelesh Pandey  

This question says, 

Which of the following can be incorrect ?

Thats why option C is taken as it is incorrect. 

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Yes..i mean to say how it is incorrect??

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@neelesh pandey

Question says maximum p courses, so take p=5 , maximum v students take v  = 2

for student table x is number of tuple so x = 5 ( as it is said at least one student per course ) and for courses table y is number of tuples , so y = 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.

For option B ,  y <= p * x put p =5 and x = 5 and y = 5 it becomes 5<= 25 that is TRUE.

For option C , x >= v *y  put x,v,y value it becomes 5 >= 2 * 5  => 5 >= 10 that is False

Thats why option C is incorrect.

Answer 1

(A) Y >= 1, must be TRUE if we assume there is at least one student  

(B) Y <= p * X, must be TRUE as a student can register for at most p courses, x student can register for  at most px courses. Assuming all these are unique, we can have maximum pX courses as there are no courses without a registered student.       

(C) X >= v *  Y, need not be TRUE as there are Y courses and each course can have at most v students.  If we replace 'at most' with 'at least' this would be TRUE.          

(D) X > 0, TRUE with same assumption as option A.

Answer 2

Question says maximum p courses, so take p=5 , maximum v students take v  = 2

for student table x is number of tuple so x = 5 ( as it is said at least one student per course ) and for courses table y is number of tuples , so y = 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.

For option B ,  y <= p * x put p =5 and x = 5 and y = 5 it becomes 5<= 25 that is TRUE.

For option C , x >= v *y  put x,v,y value it becomes 5 >= 2 * 5 that is False

Thats why option C is incorrect.

Answer 3

Each student is enrolled to at least one course and each course has at least one student.

As per this, Options A and D must be correct.

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A student can register for at most p courses

So, maximum entries in Y can be $p*number\_of\_students$

=> $Y \leq p*X$

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each course can have at most v students.

So, maximum entries in X = $v*number\_of\_courses$

=> $X \leq v*Y$

So, Option C need not be true.

Comments

What if there are 0 students and 0 courses? Is such situation possible?

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I guess we have to assume that the tables are non-empty.