# Curious question about cardinality of finite sets

by Castor   Last Updated September 11, 2019 18:20 PM - source

Suppose we are given three finite, non-empty sets $$A, B, C$$ such that $$|C|\leq |A| \leq |B|$$. Is it always true that $$\frac{|A\cap C|}{|A|} + \frac{|B\cap C|}{|B|} \leq 1 + \frac{|A\cap B|}{|B|}$$?

I have tried countless examples for days and I haven't found any counterexample so far... This is just a curious question. But if it's true, there has to be a proof, right?

Tags :