Question

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

Answer 1

Take A = {1, 2} B = {1, 4} and C = {2, 4}

Now $A\cap B$ = {1} $\ne \Phi$

$B\cap C$ = {4} $\ne \Phi$

$A\cap C$ = {2} $\ne \Phi$

But $A\cap B\cap C$ = $\Phi$