Independent Events Become Dependent Under Conditioning

Let $A$ and $B$ be independent events with $P(A) = P(B) = 1/2$. Define $D = A \triangle B$ (exactly one of $A$, $B$ occurs). (a) Compute $P(D)$, $P(A \mid D)$, and $P(A \cap B \mid D)$. (b) Are $A$ and $B$ conditionally independent given $D$? (c) Are $A$ and $B$ conditionally independent given $D^c$?