Question:
Find sets $A, B$ and $C$ such that $A \cap B, A \cap C$ and $B \cap C$ are non-empty sets and $A \cap B \cap C=\phi$.
Solution:
Let us consider the following sets,
A = {5, 6, 10 }
B = {6,8,9}
C = {9,10,11}
Clearly, $A \cap B=\{6\}$
$B \cap C=\{9\}, A \cap C=\{10\}$ and $\mathrm{A} \cap \mathrm{B} \cap \mathrm{C}=\phi$
It means that, $A \cap B, B \cap C$ and $A \cap C$ are non empty sets and $\mathrm{A} \cap \mathrm{B} \cap \mathrm{C}=\phi$