Full Idea
Most people find it hard to find any conclusion that fits the following premises: 'No councillors are bankers', and 'All bankers are athletes'. There is a valid conclusion ('Some athletes are not councillors') but it takes quite an effort to find it.
Gist of Idea
'No councillors are bankers' and 'All bankers are athletes' implies 'Some athletes are not councillors'
Source
Keith Devlin (Goodbye Descartes [1997], Ch. 2)
Book Reference
Devlin,Keith: 'Goodbye Descartes: the end of logic' [Wiley 1997], p.43
A Reaction
A nice illustration of the fact that syllogistic logic is by no means automatic and straightforward. There is a mechanical procedure, but a lot of intuition and common sense is also needed.