This question is easier to Answer With Boolean Algebra ->
$A\bigodot B= B\to A$, i.e. $(\neg B\vee A).$
now,
Lets look at Option D
$\neg (\neg A\bigodot B)$
$=\neg (B\to \neg A)$
$=\neg (\neg B\vee \neg A)$
$=B\wedge A$
So Answer is D.
Other options ->
A) $\neg B\vee \neg A$
B) $\neg B\wedge \neg A$
C) $\neg B\wedge A$