Three pieces of information must be connected.
A student participates in $\mathrm{TAKE}$ through
$\mathrm{STUDENT.regno = TAKE.regno}$.
A $\mathrm{TAKE}$ tuple identifies the course through
$\mathrm{TAKE.cno = COURSE.cno}$.
Finally, the course must satisfy $\mathrm{COURSE.dept} =$ '$\text{EECS}$'.
Therefore, form the Cartesian product:
$\mathrm{STUDENT \times TAKE \times COURSE}$
and select only those tuples satisfying all three conditions:
$\mathrm{STUDENT.regno = TAKE.regno}$
$\mathrm{TAKE.cno = COURSE.cno}$
$\mathrm{COURSE.dept} =$ '$\text{EECS}$'.
Finally, project $\mathrm{name}$.
Thus, A is correct.
B finds students whose own department is $\mathrm{EECS}$. That is a different question.
C never connects students to courses through $\mathrm{TAKE}$, so every student could be paired with an $\mathrm{EECS}$ course.
D connects a student to a $\mathrm{TAKE}$ record, but never connects that $\mathrm{TAKE}$ record to the selected $\mathrm{EECS}$ course. It can therefore generate false matches.
Hence, the correct expression is A.
