Find sets A, B and C such that

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 $\mathrm{A} \cap \mathrm{B} \cap \mathrm{C}=\phi$