Using an Euler diagram determine if the argument is valid or invalid?

Question

Some psychologists are university professors

Some psychologists have a private practice

Some university professors have private practice

P.S. So I got the diagram which is 3 circles each representing psychologists, university professors and those with private practice. So,the psychologist circle has a common region with university professors on one side and a common region with those with private practice circle on the other side. So, circles representing those with private practice and university professors don't necessarily have common region. Which means the argument should be invalid. The answer in the book shows a diagram where all the three circles have common region and says that the argument is still invalid. I'm confused here. Why is it necessary that they all have a common region and if so, why is the argument invalid then?

Answer 1

You are probably not looking at an Euler diagram, but a Venn diagram. A Venn diagram shows all possible overlaps, but just because circles overlap does not mean that they have something in common. Indeed, the information embodied in the premises can force certain of those overlapping regions to be empty .. And even if some region is not forced to be empty, that still does not mean that there has to be something in that region.