Begin with a student tuple $s$.
The output must contain the student's name:
$t.\mathrm{name}=s.\mathrm{name}$.
Now describe the condition we want to exclude.
A student is taking an EECS course if there exist:
- a $\mathrm{TAKE}$ tuple $x$
- a $\mathrm{COURSE}$ tuple $c$
such that
$x.\mathrm{regno}=s.\mathrm{regno}$
$x.\mathrm{cno}=c.\mathrm{cno}$
and
$c.\mathrm{dept}=\mathrm{'EECS'}$.
Therefore,
$\exists x\in \mathrm{TAKE};\exists c\in \mathrm{COURSE}(\cdots)$
means the student takes at least one EECS course.
We need the opposite, so negate the entire existential condition:
$\neg\exists x\in \mathrm{TAKE};\exists c\in \mathrm{COURSE}(\cdots)$.
Hence A is correct.
B returns students who do take an EECS course.
C tests the student's own department, which is unrelated to whether the courses they take are offered by EECS.
D does not connect courses to the student at all.
Therefore,
Answer : $\boxed{\mathrm{A}}$
