How to Check For Validity With Diagrams.

In Chapter 8, section B we learned how to check for validity with diagrams. I find this to be very fun and interesting to do with the examples and exercises. Some of the rules are as followed:

A collection is represented by a circle. If one circle is enveloped by another circle that means everything in that smaller circle is applied to the bigger circle. This is the crucial part. The attributes of the small circle applies to the bigger circle, it does not mean the attributes of the bigger circle applies to the smaller circle. If a circle is not bound by any circle then it is not related to anything at all. Using the same example I used in Section A.

“Only postal employees deliver U.S. mail.
Ralph is a postal employee.
So Ralph delivers U.S. mail.”

First apply the rule of Only: “Only A are B” means “All B are A.” This means deliver U.S. mail would be the smaller circle, and postal employees would be the bigger circle around it. Ralph would be another circle inside of postal employees but it doesn’t have any relation to deliver U.S. mail which means the conclusion “So Ralph delivers U.S. mail,” is not valid.