Find sets A, B and C such that A ∩ B, B ∩ C and A ∩ C are non-empty sets and A ∩ B ∩ C = Φ.
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, $A \cap B \cap C=\Phi$