## 5. In the Zoo

Let's assume that in all zoos where there are hippos and rhinos, there are no giraffes; in all zoos where there are rhinos and no giraffes, there are hippos; finally, in all zoos where there are hippos and giraffes, there are also rhinos. How do you think, can there be a zoo where there are hippos, but no giraffes or rhinos?
5. Yes, such a zoo can exist. Indeed, let $Z$ be the set of zoos, $H$ be the subset of those that have hippos, $R$ be the subset

![](https://cdn.mathpix.com/cropped/2024_05_21_fe999c0fe2ad81fc5164g-205.jpg?height=574&width=628&top_left_y=455&top_left_x=728)

of those that have rhinos, and $G$ be the subset of those that have giraffes. Let's represent all this on a Venn diagram. The first condition means that the intersection I of the sets $H$, $R$, and $G$ does not contain any elements, i.e., it is empty. Due to the second condition, the set II of zoos that have rhinos but no giraffes or hippos is empty, and due to the third condition, the set III of zoos that have hippos and giraffes but no rhinos is empty. However, this does not mean that the set IV of zoos with hippos but without giraffes and rhinos must be empty!