Answer
$counter\,\,example\,\,:\\
A=\left \{ 1,2 \right \},B=\left \{ 4,5 \right \},C=\left \{ 1,2,3 \right \}\\
$
Work Step by Step
$For\,\,all\,\,sets\,\,A,\,B,\,and\,\,C\,\\
if\,A\nsubseteq B \,and\,B\nsubseteq C\,then\,A\nsubseteq C \\
this\,\,is\,\,not\,\,true:\\
counter\,\,example\,\,:\\
A=\left \{ 1,2 \right \},B=\left \{ 4,5 \right \},C=\left \{ 1,2,3 \right \}\\
notice\,\,that\,\,A\nsubseteq B\,\,and\,B\nsubseteq C \\
\left \{ 1,2 \right \}\nsubseteq \left \{ 4,5 \right \},\left \{ 4,5 \right \}\nsubseteq \left \{ 1,2,3 \right \}\\
but \,\, A\subseteq C \,\,\,\left \{ 1,2 \right \}\subseteq \left \{ 1,2,3 \right \}
$