GO Classes DPP | GATE CS, DA | DBMS | Relational Division

Answer 1

Division answers a query of the form:

Find every $X$ that is associated with every required $Y$.

Here:

• $X = \mathrm{student\ name}$

• $Y = \mathrm{course\ taught\ by\ Elizabeth\ Taylor}$

First determine exactly the required courses:

$\mathrm{ET} = \rho_{\mathrm{ET}(\mathrm{cname})}\left(\pi_{\mathrm{name}}\left(\sigma_{\mathrm{fname}=\text{'Elizabeth Taylor'}}(\mathrm{Class} \bowtie \mathrm{Faculty})\right)\right)$

The rename is important because the divisor attribute must correspond to $\mathrm{cname}$.

Next construct the student-course pairs:

$\mathrm{SE} = \pi_{\mathrm{sname},\mathrm{cname}}(\mathrm{Student} \bowtie \mathrm{Enrolled})$

Now,

$\mathrm{SE} / \mathrm{ET}$ returns each $\mathrm{sname}$ that occurs with every $\mathrm{cname}$ in $\mathrm{ET}$.

Thus A is correct.

C requires only at least one course taught by Elizabeth Taylor, not every such course.

D incorrectly requires students to have taken every course in the complete $\mathrm{Class}$ relation.

Answer : A