Just use a Venn Diagram

Probability Level 1

Given 3 distinct sets $A$ , $B$ and $C$ , is it possible that

$A \cap B = B \cap C = C \cap A?$

No Yes

2 solutions

Rishabh Jain
Jan 23, 2016

Clearly in this case A $\cap$ B=B $\cap$ C=C $\cap$ A

Venkata Karthik Bandaru
Jan 23, 2016

One can have $3$ mutually disjoint sets, so that $A \cap B = B \cap C = C \cap A = \phi$ .

That's a good example. What if we want the intersection to be non-empty?