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

Is composite attribute is same as prime attribute?

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Prime attributes are the attributes of the candidate key which defines the uniqueness (Eg: SSN number in a employee database).

A composite attribute is one that is composed of smaller parts. An atomic attributeis indivisible or indecomposable. Example : A BirthDate attribute can be viewed as being composed of (sub-)attributes month, day, and year (each of which would probably be viewed as being atomic). Name is composite attribute- middle name, first name, last name .

so both are Not equal.

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How the answer is 3NF please explain?

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The question is wrong here. With the given information, the relation is sure to be only 1NF as details of no other FDs are given. IT should be "the relation is not in" and answer being BCNF.

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changed the question .

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How option(c) is correct??

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@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.