Solution
= Solution
Take every <complement of a set> relative to $\mathcal U$. By <set difference>, <De Morgan's laws>, and distribution of <set intersection> over <set union>,
$$
\begin{aligned}
A\setminus(B\cap A\cap C)
&=A\cap(B^c\cup A^c\cup C^c)\\
&=(A\cap B^c)\cup(A\cap A^c)\cup(A\cap C^c)\\
&=A\cap(B^c\cup C^c)\\
&=\boxed{A\setminus(B\cap C)}.
\end{aligned}
$$
Here the middle term is the <empty set>, since a <set> and its <complement of a set> are disjoint.