Question

Find sets A, B and C such that $A\cap B,B\cap C$ and $A\cap C$ are non-empty sets and $A\cap B\cap C=\varphi$

Answer 1

Let $A=\{0,1\},B=\{1,2\}$, and $C=\{2,0\}$
Accordingly,
$A\cap B=\left\{1\right\}$
$B\cap C=\left\{2\right\}$
$A\cap C=\left\{0\right\}$.
$\therefore A\cap B,B\cap C$, and $A\cap C$ are non-empty.
However, $A\cap B\cap C=\varphi$