Question

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

Answer 1

To find sets A, B and C such that $A\cap B\ne \varphi$, $A\cap C=\varphi$ and $B\cap C=\varphi$ and $A\cap B\cap C=\varphi$

Take A = {1,2,3}

B= {2,4,6}

and C = {3,4,7}

Then,

$A\cap B=$ {2}

$\therefore A\cap B\ne \varphi$

$A\cap C=$ {3}

$\therefore A\cap C\ne \varphi$

$B\cap C=$ {4}

$\therefore B\cap C\ne \varphi$

Howver A, B and C have no elements in common.

$\therefore A\cap B\cap C=\varphi$