Answer
$For\,\,all\,\,sets\,\,A,\,B,\,\,and\,C\,\,\\
if\,\,A \cap B = \varnothing\,\,then\,\,A \times B = \varnothing.\\
this\,\,is\,\,\,false\\
counter\,\,example\,\,:\\
A=\left \{ 7 \right \},B=\left \{ 8 \right \}\\
A\cap B=\left \{ 7 \right \}\cap \left \{ 8 \right \}=\varnothing \\
But\,\,A \times B=\left \{ \left ( 7,8 \right ) \right \}\neq \varnothing
$
Work Step by Step
$For\,\,all\,\,sets\,\,A,\,B,\,\,and\,C\,\,\\
if\,\,A \cap B = \varnothing\,\,then\,\,A \times B = \varnothing.\\
this\,\,is\,\,\,false\\
counter\,\,example\,\,:\\
A=\left \{ 7 \right \},B=\left \{ 8 \right \}\\
A\cap B=\left \{ 7 \right \}\cap \left \{ 8 \right \}=\varnothing \\
But\,\,A \times B=\left \{ \left ( 7,8 \right ) \right \}\neq \varnothing
$