Question

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

• A. $A=\{0,1\},B=\{1,2\}$ and $C=\{3,0\}$
• B. $A=\{0,1\},B=\{-1,2\}$ and $C=\{2,0\}$
• C. $A=\{-1,1\},B=\{1,2\}$ and $C=\{4,0\}$
• D. $A=\{0,1\},B=\{1,2\}$ and $C=\{2,0\}$

Answer 1

The correct option is D $A=\{0,1\},B=\{1,2\}$ and $C=\{2,0\}$

Let, $A=\{0,1\},B=\{1,2\}$ and $C=\{2,0\}$
Accordingly, $A\cap B=\left\{1\right\},B\cap C=\left\{2\right\}$ and $C\cap A=\left\{0\right\}$
$\therefore$ $A\cap B,B\cap C$ and $C\cap A$ are non-empty sets.
However, $A\cap B\cap C=\varphi .$