Question:
Find sets $A, B$ and $C$ such that $A \cap B, B \cap C$ and $A \cap C$ are non-empty sets and $A \cap B \cap C=\Phi$.
Solution:
Let $A=\{0,1\}, B=\{1,2\}$, and $C=\{2,0\}$.
Accordingly, $A \cap B=\{1\}, B \cap C=\{2\}$, and $A \cap C=\{0\} .$
$\therefore A \cap B, B \cap C$, and $A \cap C$ are non-empty.
However, $A \cap B \cap C=\Phi$
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