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

Find sets $A,B\text{and}C$ for given condition.
$A\cap B,B\cap C$ and $A\cap C$ are non-empty sets and $A\cap B\cap C=\varphi$

Let $A=\{0,1\},B=\{1,2\}\text{and}C=\{2,0\}$
So, $A\cap B=\{0,1\}\cap \{1,2\}=\left\{1\right\}$
$B\cap C=\{1,2\}\cap \{2,0\}=\left\{2\right\}$
and $A\cap C=\{0,1\}\cap \{2,0\}=\left\{0\right\}$

$\therefore A\cap B,B\cap C$ and $A\cap C$ are non-empty sets.
However, $A\cap B\cap C=\varphi$