Question

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

Answer 1

Let A = {0, 1}, B = {1, 2}, and C = {2, 0}.
Accordingly, $A ∩ B =$ {1}, $B ∩ C =$ {2}, and $A ∩ C =$ {0}.
$∴ A ∩ B, B ∩ C,$ and $A ∩ C$ are non-empty.
However, $A ∩ B ∩ C = \phi$