Answer
$A=\left \{ 1,2,3,4 \right \},B=\left \{ 2,3 \right \},C=\left \{ 3,4 \right \}\\
$
Work Step by Step
$For\,\,all\,\,sets\,\,A,\,B,\,and\,\,C\,\\
if\,\,B\cap C\subseteq A\\
\,\,then\,(A-B)\cap(A-C)=\varnothing \\
this\,\,is\,\,not\,\,true:\\
counter\,\,example\,\,:\\
A=\left \{ 1,2,3,4 \right \},B=\left \{ 2,3 \right \},C=\left \{ 3,4 \right \}\\
B\cap C=\left \{ 3 \right \}\subseteq \left \{ 1,2,3,4 \right \}=A \\
A-B=\left \{ 1,4 \right \},A-C=\left \{ 1,2 \right \}\\
but\,\,\\(A-B)\cap(A-C)=\left \{ 1,4 \right \}\cap \left \{ 1,2 \right \}=\left \{ 1 \right \}\neq \varnothing
$
