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?

- Serverfault Help
- Superuser Help
- Ubuntu Help
- Webapps Help
- Webmasters Help
- Programmers Help
- Dba Help
- Drupal Help
- Wordpress Help
- Magento Help
- Joomla Help
- Android Help
- Apple Help
- Game Help
- Gaming Help
- Blender Help
- Ux Help
- Cooking Help
- Photo Help
- Stats Help
- Math Help
- Diy Help
- Gis Help
- Tex Help
- Meta Help
- Electronics Help
- Stackoverflow Help
- Bitcoin Help
- Ethereum Help