I am trying to simplify this logical expression. This is what I have so far but I went wrong somewhere as the answer should be $A \oplus B$ I believe.
$\neg \overbrace{(A \lor B)}^{c} \lor \neg \overbrace{(A \land B)}^{d} \equiv$
$\neg (c \lor d) \equiv$ DeMorgan's
$c \oplus d \equiv$
$(A \lor B) \oplus (A \land B)$
How can I simplify this expression further?
You made a tiny error in your first step when applying DeMorgan's law. DeMorgan's law is the statement that $(¬x ∨ ¬y) ⟺ ¬(x ∧ y)$, or equivalently that $(¬x ∧ ¬y) ⟺ ¬(x ∨ y)$. So your first step should be $¬(c ∧ d)$ rather than $¬(c ∨ d)$. Do you think you can take it from there?