= Solution
Write $C^c=\mathcal U\setminus C$. The rules for <set difference>, <set intersection>, and <complement of a set> give
$$
\begin{aligned}
(A\cap B)\setminus(A\cap C)
&=(A\cap B)\cap(A\cap C)^c\\
&=(A\cap B)\cap(A^c\cup C^c)\\
&=(A\cap B\cap A^c)\cup(A\cap B\cap C^c)\\
&=\varnothing\cup\bigl(A\cap(B\cap C^c)\bigr)\\
&=\boxed{A\cap(B\setminus C)}.
\end{aligned}
$$
The second step is <De Morgan's laws>; the third distributes <set intersection> over <set union>. The fourth uses $A\cap A^c=\varnothing$.
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